Gr 10 Math Term 4 Test

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What is the new volume of a cylinder when the radius is multiplied by a factor of k?

$kV$
$k^2V$ (correct)
$k^3V$
$k^2V_k$

If the height of a cylinder is multiplied by k, how does it affect the surface area?

Surface area is divided by $k$
Surface area is multiplied by $k$ (correct)
Surface area is multiplied by $k^2$
Surface area remains the same

What happens to the surface area of a cylinder if both the radius and height are multiplied by k?

Surface area is multiplied by $k^3$ (correct)
Surface area is multiplied by $k$
Surface area is multiplied by $k^2$
Surface area remains constant

In terms of the volume of a cylinder, what is the relationship when only the height is increased by a factor of k?

Volume increases by $k$ (B) Signup and view all the answers

If the radius of a cylinder is multiplied by k and then the height is unchanged, which of the following can be concluded about the volume?

Volume will increase to $k^2V$ (D) Signup and view all the answers

What is the formula for the area of a triangle?

A = ½ × b × h (D) Signup and view all the answers

How do you calculate the surface area of a cylinder?

Add the areas of two circles and a rectangle (A) Signup and view all the answers

Which of the following shapes is NOT classified as a right prism?

Pyramid (A) Signup and view all the answers

Which formula represents the volume of a right prism?

Volume = area of base × height (A) Signup and view all the answers

What is the area formula for a circle?

A = πr² (D) Signup and view all the answers

What distinguishes a right pyramid from an ordinary pyramid?

The apex is directly above the base center (B) Signup and view all the answers

How is the volume of a triangular prism calculated?

Volume = ½ × base × height of triangle × height of prism (D) Signup and view all the answers

Which definition best describes the surface area of a prism?

It is the total area of the outer surfaces of the prism (B) Signup and view all the answers

What is the term used for an individual item in a sequence?

Term (D) Signup and view all the answers

Which of the following best describes a linear sequence?

A sequence with a common difference between each term (C) Signup and view all the answers

In the general formula for a linear sequence, what does the variable 'd' represent?

The difference between successive terms (B) Signup and view all the answers

What is the formula used to determine the common difference 'd' in a sequence?

d = T_n - T_{n-1} (D) Signup and view all the answers

What does the notation $T_n$ represent in a sequence?

The nth term in the sequence (D) Signup and view all the answers

If the first term of a linear sequence is 5 and the common difference is 3, what is the second term?

8 (B) Signup and view all the answers

Which statement is true about the area of a polygon?

It refers to the space inside the boundary of a flat object. (C) Signup and view all the answers

Which of the following is NOT a key point about sequences?

All sequences follow the same formula. (C) Signup and view all the answers

What is the formula for the surface area of a right cone?

$ ext{Surface Area} = ext{Area of base} + ext{Area of walls} = \pi r (r + h)$ (B) Signup and view all the answers

How will the volume of a square pyramid change when all its dimensions are multiplied by a factor of 3?

The volume is multiplied by 27 (D) Signup and view all the answers

What is the formula for the surface area of a sphere?

$4 ext{π}r^2$ (D) Signup and view all the answers

What happens to the surface area of a rectangular prism when two dimensions are multiplied by 5?

It is multiplied by 25 (D) Signup and view all the answers

What is the correct expression for the volume of a right cone?

$rac{1}{3} imes ext{Area of base} imes ext{Height of cone}$ (A) Signup and view all the answers

When one dimension of a prism is multiplied by k, how is the volume affected?

The volume is multiplied by k (A) Signup and view all the answers

For a triangular pyramid, what is the expression for its surface area?

$rac{1}{2} b (h_b + 3h_s)$ (D) Signup and view all the answers

If a sphere's radius is doubled, what is the factor by which its surface area increases?

4 (B) Signup and view all the answers

What expression represents the volume of a triangular pyramid?

$rac{1}{3} imes rac{1}{2} b h imes H$ (A) Signup and view all the answers

What happens to the volume of a cylinder when both the radius and height are multiplied by a factor of k?

The volume becomes $k^3V$ (D) Signup and view all the answers

How does the surface area of a cylinder change when only the radius is multiplied by k?

The surface area becomes $k^2A$ (D) Signup and view all the answers

If the height of a cylinder is doubled, which expression accurately represents the new surface area?

Surface Area = $kA$ where k=2 (D) Signup and view all the answers

What is the correct relationship between alterations in the height and volume of a cylinder when height is multiplied by k?

The volume increases by a factor of $k$ (B) Signup and view all the answers

Which statements correctly describe the effects of multiplying only the height of a cylinder by k?

Volume becomes $kV$, Surface Area becomes $kA$ (A) Signup and view all the answers

What does the term 'common difference' in a sequence refer to?

The constant difference between each term and the preceding term. (C) Signup and view all the answers

In the general formula for a linear sequence, $T_n = dn + c$, what does the variable 'c' represent?

The constant added to the product of 'd' and 'n'. (A) Signup and view all the answers

How can the $n$th term of a linear sequence be expressed if the first term ( $T_1$ ) is 2 and the common difference (d) is 5?

2 + 5n (B) Signup and view all the answers

If the 4th term of a sequence is 26 and the common difference is 4, what is the first term?

10 (B) Signup and view all the answers

What is the formula used to calculate the common difference 'd' in a sequence?

d = T_n - T_{n-1} (B) Signup and view all the answers

What defines a linear sequence?

It has a constant difference between successive terms. (D) Signup and view all the answers

If a sequence progresses as follows: 4, 7, 10, ..., what is the common difference?

3 (D) Signup and view all the answers

What denotes the notation $T_n$ in a sequence?

The $n$th term of the sequence. (D) Signup and view all the answers

What is the surface area formula for a triangular prism?

2 triangles and 3 rectangles (C) Signup and view all the answers

Which of the following shapes has a volume calculated by the formula $V = \pi r^2 h$?

Cylinder (C) Signup and view all the answers

For a cube with a side length of $s$, how is the volume expressed?

s × s × s (B) Signup and view all the answers

What defines a right prism?

Base and top are the same shape and size with perpendicular sides (C) Signup and view all the answers

What is the area formula for a trapezium?

A = ½ × (a + b) × h (A) Signup and view all the answers

Which property is true for a right pyramid?

The apex is located directly above the base center. (B) Signup and view all the answers

What is the circumference formula for a circle?

C = 2πr (D) Signup and view all the answers

How is the volume of a right cone calculated?

V = (1/3)πr²h (A) Signup and view all the answers

What is the surface area formula for a triangular pyramid?

$\frac{1}{2} b (h_b + 3h_s)$ (C) Signup and view all the answers

If the height of a square pyramid is multiplied by a factor of 2, by what factor does its volume change?

2 (B) Signup and view all the answers

What is the relationship between the surface area and volume when all dimensions of a rectangular prism are multiplied by 3?

Surface area increases by a factor of 9, volume increases by a factor of 27 (A) Signup and view all the answers

What is the surface area of a sphere with a radius of 4?

$64\pi$ (D) Signup and view all the answers

When only one dimension of a cone is multiplied by 4, how does its volume change?

Increases by a factor of 4 (A) Signup and view all the answers

For a right cone, what is the surface area formula if the radius is $r$ and the height is $h$?

$\pi r^2 + \pi r h$ (D) Signup and view all the answers

What is the volume of a triangular pyramid with a base area of 10 and height of 5?

$\frac{50}{3}$ (C) Signup and view all the answers

How does the surface area of a rectangular prism change when all three dimensions are multiplied by a factor of 2?

Increases by a factor of 4 (D) Signup and view all the answers

What is the volume formula for a sphere with radius $r$?

$\frac{4}{3} \pi r^3$ (C) Signup and view all the answers

What characterizes a linear sequence regarding its terms?

The terms follow a specific order with a constant difference. (C) Signup and view all the answers

If the formula for a sequence is given by $T_n = 3n + 2$, what is the common difference?

3 (B) Signup and view all the answers

In a sequence where the first term is 10 and the common difference is -4, what is the 5th term?

-6 (B) Signup and view all the answers

Which of the following statements is incorrect regarding the common difference in a sequence?

The common difference must be an integer. (B) Signup and view all the answers

What is the general formula for the $n$th term of a linear sequence if the constant is -7?

$T_n = dn + (-7)$ (A) Signup and view all the answers

Given the sequence represented as 2, 5, 8, 11, ..., which term of the sequence corresponds to the value of 32?

11th term (A) Signup and view all the answers

How do you determine the general term formula for a sequence starting at 7 with a common difference of 3?

$T_n = 3n + 7$ (D) Signup and view all the answers

If a sequence is described as having a first term of 1 and a common difference of 0, what can be inferred about its terms?

The terms will be constant. (C) Signup and view all the answers

What is the formula for the volume of a right prism with a triangular base?

$V = rac{1}{2} b h_{triangle} h$ (D) Signup and view all the answers

Which statement correctly describes the surface area calculation of a cylinder?

It is the sum of the areas of two circles and the area of one rectangle. (D) Signup and view all the answers

What distinguishes a right cone from other types of cones?

The apex of the cone is directly above the center of the base. (A) Signup and view all the answers

Which of the following statements about volume is true for right prisms?

Volume is determined by the area of the base multiplied by the height. (C) Signup and view all the answers

How is the area of a trapezium defined mathematically?

$A = rac{1}{2} (b_1 + b_2) h$ (A) Signup and view all the answers

What is the key characteristic of a sphere regarding its dimensions?

It appears the same from any angle. (D) Signup and view all the answers

In the formula for the volume of a cylinder, which variable represents the height?

$h$ (C) Signup and view all the answers

What characteristic defines a right pyramid?

Its apex is directly above the center of the base. (D) Signup and view all the answers

What is the factor by which the volume of a cylinder is changed when both the radius and height are multiplied by k?

k^3 (B) Signup and view all the answers

How does the surface area of a cylinder change when the height is doubled and the radius remains constant?

Increases by a factor of 2 (B) Signup and view all the answers

If the radius of a cylinder is multiplied by k, by what factor does the surface area increase?

k^2 (A) Signup and view all the answers

What happens to the volume and surface area of a cylinder if the height is multiplied by k and the radius is also multiplied by k?

Volume changes by k^3 and surface area by k^2 (C) Signup and view all the answers

If the radius of a cylinder is increased by a factor of k and the height is decreased by a factor of k, what is the overall effect on the volume?

Volume increases by a factor of k (A) Signup and view all the answers

What happens to the volume of a square pyramid when the height is multiplied by a factor of 3?

It is multiplied by 3. (A) Signup and view all the answers

If the radius of a right cone is doubled while the height remains unchanged, what is the new surface area?

It increases fourfold. (A) Signup and view all the answers

When all dimensions of a triangular pyramid are multiplied by a factor of 2, by what factor does the surface area increase?