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Questions and Answers

Factorise 2x+10+dx+5d

  • None of these
  • (x+5)(2+d)
  • (x+10)(+5)
  • (x+d)(2+5)
  • (x+2)(5+d) (correct)

Identify the correct expression of x using trigonometry

  • 6 tan 72°
  • 15 Sin 72° (correct)
  • None of these
  • 6 Cos 72°
  • 15 Cos 72°

Find the value of x

15 72° x 6

  • 3√21 (correct)
  • 9
  • None of these
  • 3/29
  • 18

Expand and simplify 3x(x + 1) + x(x-4)

<p>4x²-x (A)</p> Signup and view all the answers

Identify the coordinates of the turning point of the graph below:

                A

<p>(1,3) (A)</p> Signup and view all the answers

Rationalise and Simplify: 6√3 √2

<p>3√6 (C)</p> Signup and view all the answers

If x 2

3

x² = y

2

4

= z, calculate: x ÷ z - y

<p>2 7 (D)</p> Signup and view all the answers

Note that 280 ÷ 1.4 = 200. So, 28 ÷ 0.14 =

<p>20 (E)</p> Signup and view all the answers

An American picture book has a picture of a kitten in it, which is 25 inches. How tall is the kitten in centimetres?

<p>63.5 (A)</p> Signup and view all the answers

Study first triangle to identify the value of Z in the second triangle.

5

3

4

10

8 Z

<p>6 = 10 7 = 3 4 = 4 2 = 8</p> Signup and view all the answers

How many students were surveyed?

<p>37 (C)</p> Signup and view all the answers

How many students played tennis only?

<p>13 (A)</p> Signup and view all the answers

How many students neither played tennis nor badminton?

<p>2 (B)</p> Signup and view all the answers

The swimming pool is about 1.5 metres deep. If the diagram below shows the swimming pool, how much water (in litres) would be required to fill the pool to the very top?

1.8 m

1.1 m

<p>3000L (E)</p> Signup and view all the answers

Simplify: (4√3-√5)²

<p>53-4√15 (C)</p> Signup and view all the answers

A tin of paint costs $3.2 and it can paint 450 square meter. If a room has a rectangular wall with dimensions of 43.2m x 29.1m, how many tins of paint would a painter need? Select the appropriate calculation.

<p>43.2×29.1 450×3.2 (E)</p> Signup and view all the answers

Last Sunday, there was a medical conference and the audience consisted of doctors and researchers. 240 of the audience were researchers. This was 60% of the total number of audience. What is the total number of audience at the conference?

<p>384 (A)</p> Signup and view all the answers

Continued from question 17: How many doctors were there?

<p>144 (B)</p> Signup and view all the answers

A number z is squared and is subtracted from three times its cube. If the result is 33, select the appropriate equation to identify the value of number Z.

<p>3(z³ - z²) = 33 (C)</p> Signup and view all the answers

Identify the set of coordinates of the point that lie inside the shaded area.

10 (0,10) 8 6 4 (1,3) 2 0 -2 -4 (2,-4) 2 The linear graph passes through the points: (0,10), (1,3) and (2,-4)

<p>(2, 4) (C)</p> Signup and view all the answers

Identify the set of coordinates of the point that lie outside the shaded area.

10 (0,10) 8 6 4 (1,3) 2 0 -2 -4 (2,-4) 2 The linear graph passes through the points: (0,10), (1,3) and (2,-4)

<p>(-1,3) (B)</p> Signup and view all the answers

Identify the gradient of the linear graph.

10 (0,10) 8 6 4 (1,3) 2 0 -2 -4 (2,-4) 2 The linear graph passes through the points: (0,10), (1,3) and (2,-4)

<p>-7 (A)</p> Signup and view all the answers

Identify the equation of the linear graph.

10 (0,10) 8 6 4 (1,3) 2 0 -2 -4 (2,-4) 2 The linear graph passes through the points: (0,10), (1,3) and (2,-4)

<p>y = -7x + 10 (E)</p> Signup and view all the answers

Tim was paid $313 after working 20 hours. What is the hourly pay?

<p>15.65 (D)</p> Signup and view all the answers

What is the intersection point of the two graphs of y = 3 - 2x and y = x²?

<p>(1,1) (D)</p> Signup and view all the answers

Laura started reading a book at 2:55pm. If she read a book for 2 1 2 hours, what time did she finish reading a book?

<p>5:25pm (A)</p> Signup and view all the answers

If each individual square has an area of 1.44cm², what is the size of the length of this square?

<p>1.2cm (A)</p> Signup and view all the answers

What is the area of the triangle?

<p>6.48cm² (C)</p> Signup and view all the answers

What is the area of the circle? (use π = 3.14)

<p>10.17cm² (E)</p> Signup and view all the answers

Simplify (2w + 4)(2w – 4)

<p>4w² - 16 (B)</p> Signup and view all the answers

-(-4)³ =

<p>64 (E)</p> Signup and view all the answers

If A B(C-4) 2D AB+4 what is C?

<p>2AD B (E)</p> Signup and view all the answers

What is the volume of the rectangular prism?

5cm

2cm

7cm

<p>70cm³ (B)</p> Signup and view all the answers

What is the mass of the rectangular prism, given that Density= Mass + Volume? Note that density = 1.4gm /cm³

5cm

2cm

7cm

<p>165.2gm (B)</p> Signup and view all the answers

What is the surface area of the rectangular prism?

5cm

2cm

7cm

<p>118cm² (E)</p> Signup and view all the answers

Jo wants to giftwrap a present that has the same dimension as the rectangular prism in the above diagram. If the giftwrapping paper costs $0.42 per 20cm², how much will it cost her to buy the required area of giftwrapping paper?

5cm

2cm

7cm

<p>$2.40 (D)</p> Signup and view all the answers

What is the probability that a total of 7 is thrown, if two six sided dice are thrown together?

<p>None of these (A)</p> Signup and view all the answers

Which equation is most likely to be the equation of the graph below?

y

x

<p>y = -2x + 3 (E)</p> Signup and view all the answers

Given that the x-intercept is (2,0) and y-intercept is (0,-5) for the linear graph of question 38, identify the gradient.

<p>-2.5 (E)</p> Signup and view all the answers

(2xº)×(3x3)º

<p>2 (A)</p> Signup and view all the answers

212 can be also written as

<p>(√21)² (C)</p> Signup and view all the answers

3y² 6x³

  x

  4x xy³

9xy² 9x² 9x 9y²

2

y

2y

2x

<p>9xy² 2y (D)</p> Signup and view all the answers

The refrigerator my mum wanted to buy is $2400 at Harvey Norman. My friend who works at Good Guys, can give her a 15% discount. What is the discounted price of the refrigerator at Good Guys?

<p>$2040 (E)</p> Signup and view all the answers

If the pattern continues down the table, the number in column IV and row E would be:

II III IV
A 3 5 7 9
B 13 15 17 23
E

<p>49 (C)</p> Signup and view all the answers

The number 77 would be in

II III IV
A 3 5 7 9
B 13 15 17 23
E

<p>Column VII, Row G (E)</p> Signup and view all the answers

Flashcards

Factorise 2x + 10 + dx + 5d

Find the factors of the expression 2x + 10 + dx + 5d by grouping terms to extract common factors.

Expression of x using trigonometry in a triangle

Use trigonometric ratios (sine, cosine, or tangent) to relate the known side and angle to the unknown side (x) in a right-angled triangle.

Calculate the value of x

Use the given triangle and trigonometry to compute the value of x

Expand and Simplify 3x(x + 1) + x(x − 4)

Distribute the terms, combine like terms, and simplify the resulting expression.

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Coordinates of the turning point

Find the point where a graph changes direction from increasing to decreasing or vice versa.

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Rationalize and Simplify

Express a fraction with a surd in the denominator as an equivalent fraction with a rational denominator.

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Calculate x ÷ z − y

Substitute values for x, y, and z, then perform division, subtraction in given order..

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Calculate 28 ÷ 0.14 given 280 ÷ 1.4 = 200

Relate the division of 28 by 0.14 to the division of 280 by 1.4

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Convert inches to centimetres

Convert a length given in inches to an equivalent length in centimetres, knowing 1 inch = 2.54 cm

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Find the value of Z in a triangle

Determine the unknown side length of a triangle using similar triangles.

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Total number of students surveyed

Find the total number of students who participated in the survey.

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Students played tennis only?

Find the number of students who only participated in tennis.

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Students neither playing tennis nor badminton?

Find the number of students who did not participate in either tennis or badminton.

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Water volume of a swimming pool

Calculate the volume of water needed to fill a swimming pool; use the measurement of length, width and depth of a swimming pool in a standard calculation unit.

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Simplify (4√3 − 5√)

Combine like terms with square roots to simplify the expression.

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Calculate the number of paint tins needed?

Calculate the surface area of a rectangular wall, and then divide by the area each tin can cover to find the number of paint tins needed.

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Calculate the total number of audience at a conference

Find the total number of people who attended a medical conference, given a percentage of the attendees are researchers.

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Calculate the number of doctors at a conference

Calculate the number of doctors at a medical conference, given the total number of attendees and the number of researchers at the conference.

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Equation to identify the value of z

Define the expression by creating an equation to describe the situation with a given variable and mathematical operations, then solve through algebraic manipulation.

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Study Notes

Maths Test Set 01

  • Question 1: Factorise 2x + 10 + dx + 5d = (x + 5)(2 + d)

  • Question 2: Using trigonometry, x = 6 tan 72°

  • Question 3: Value of x in triangle = 18

  • Question 4: Expand and simplify 3x(x + 1) + x(x - 4) = 4x² - x

  • Question 5: Coordinates of turning point of graph = (-1, -3)

  • Question 6: Rationalise and simplify 6√3/√2 = 3√6

  • Question 7: Calculate x ÷ z - y with given values.

  • Question 8: 28 ÷ 0.14 = 200

  • Question 9: Kitten's height in centimetres = 50.5cm

  • Question 10: Value of Z in second triangle of given image = 7

  • Question 11: Number of surveyed students = 46

  • Question 12: Number of students who played tennis only = 8

  • Question 13: Number of students who played neither tennis nor badminton = 4

  • Question 14: Pool water required (litres) = 2700L

  • Question 15: Simplify (4√3 - √5)² = 53 - 8√15

  • Question 16: Number of tins of paint needed = 10.24

  • Question 17: Total number of audience at the conference = 400

  • Question 18: Number of doctors at the conference = 160

  • Question 19: Equation for value of z = 3z³ - z² = 33

  • Question 20: Coordinates inside shaded area = (1,6)

  • Question 21: Coordinates outside shaded area = (-1,-2)

  • Question 22: Gradient of the linear graph = -7

  • Question 23: Equation of the linear graph = y = -7x + 10

  • Question 24: Hourly pay = $15.65

  • Question 25: Intersection point of the two graphs = (3,3)

  • Question 26: Time Laura finished reading = 5:15pm

  • Question 27: Length of each square = 1.2cm

  • Question 28: Area of triangle = 5.04cm²

  • Question 29: Area of a circle = 11.31cm²

  • Question 30: Simplified expression = (2w + 4)(2w - 4) = 4w² - 16

  • Question 31: Calculation: -(-4)³ = 64

  • Question 32: Value of C from the equation = 2(AD)/B+4

  • Question 33: Volume of rectangular prism = 70cm³

  • Question 34: Mass of rectangular prism = 98gm

  • Question 35: Surface area of rectangular prism = 90cm²

  • Question 36: Cost of giftwrapping paper = $2.40

  • Question 37: Probability of throwing a 7 with two 6-sided dice = 1/9

  • Question 38: Equation of the graph = y = -2x + 3

  • Question 39: Gradient of the linear graph = -2.5

  • Question 40: (2xº) × (3x³) = 6x³

  • Question 41: 21½ = (√21)²

  • Question 42: Simplified expression = 2y/3x.

  • Question 43: Discounted price of the refrigerator = $2040

  • Question 44: Number in column IV, row E = 41

  • Question 45: Number 77 is in Column III, Row H

  • Question 46: Date after 17th September (Thursday) Tomorrows = 23rd September

  • Question 47: Brother's birth year = 1983

  • **Question 48:**Simplified = 4√10

  • Question 49: New value of Peter's phone = $900

  • Question 50: Shape = Triangular based pyramid

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