Year 7 Maths Test (PDF)

Maths Test Yr 7 AT3/4 :) Algebraic Techniques Ex 8E to 8L - 8E When multiplying in algebra we collect coefficients and pronumerals so 5 x X x 2 x y = 10xy. When dividing we simplify the coefficients - 8F Expanding Brackets a(b+c) = ab+ac - 8G Applying Algebra - Make...

Maths Test Yr 7 AT3/4 :) Algebraic Techniques Ex 8E to 8L - 8E When multiplying in algebra we collect coefficients and pronumerals so 5 x X x 2 x y = 10xy. When dividing we simplify the coefficients - 8F Expanding Brackets a(b+c) = ab+ac - 8G Applying Algebra - Make sure pronumerals are clearly defined. - 8I & 8J Number Patterns - look for common distance, ratio, interlinked patterns and special patterns (squares, cubes, roots, etc.) - 8L Cartesian Plane - x - input, y - output, input is plotted before output, x before y, (crawl before you walk). Decimals Ex 4G, 4H, 4I, 4K, 4N, 6A, 6E, 6F, 6H - 4G Place Value - Thousands, Hundreds, Tens, Ones (.) tenths, hundreths, thousandths - 4H ROunding Decimals - 4 or below, round down, 5 or above round up (question will say to round to nearest decimal place) - 4I Decimal Fraction Conversion - decimal can be numerator, denominator as power of ten (e.g. 3.25 = 3 & 25/100 - 3&¼) Make sure to convert the fraction denominator to a power of 10, the to a decimal. (e.g. ⅖ x2 4/10 - 0.4). A dot above the decimal means recurring, - 4K Decimal Percentage Conversion - percentage to decimal, divide by 100. Decimal to percentage - x100 - 6A Adding or subtracting decimals, keeping decimal points in the same spot, use an algorithm. - 6E Multiplying and Dvindigin by Powers of 10 - 10n means 1 followed by n zeroes. So, 104 is 1000. - 6F Multiplying a decimal - multiply as usual, placing the decimal place according to the number of decimal places in the question. When Multiplying by powers of ten, move the decimal place according to the number of 0. - 6H Dividing by a decimal - dividing by a whole number, keep decimal point place, when dividing by a decimal, make number dividing by a whole number (move both decimal places), when dividing by power of 10, remove zeroes and do division normal, then move the decimal place according to the number of zeroes Angles and Geometry Ex 2A to 2E and 6C, 6D, 6F - 2A Points Lines and Intervals - point, labelled with capital letter, line no endpoints, ray - line one end point, segment - line two endpoints, plane - flat surface no ends, collinear three or more points on a line, concurrent lines three or more lines intersecting at a point, intersections - two lines cross at a point, vertex - corner of an angle, parallels lines - lines that never meet, perpendicular - lines crossing, complimentary, angles add up to 90 degrees, supplementary - angles add up to 180 degrees, - 2D Transversal and parallel lines - a transversal line - intersecting two or more lines (mostly parallel), corresponding angles, alternate angles, co interior lines (must make 180 degrees) - 6C Triangles - triangles have 3 sides, vertices and interior angles. Triangle angles add up to 180 degrees. Area of the triangle is ½ bh. Scalene - all different sides, isosceles - two different sides, equilateral - all the same sides. Exterior angle is equal to the sum of two opposite interior angles (bac + abc = acd) - 6D Quadrilaterals - convex - all angles are pointing outwards, non-convex - one vertex pointing inwards, angles sum - all angles add up to 360 degrees. - 6F Line symmetry and rotational symmetry - line symmetry divides a shape into two equal parts. Rotational symmetry is how many times you can see the original shape when rotating 360 degrees. (e.g. square is 4) If it has no rotational symmetry, we say its order is one. Equations Ex 9A to 9H - 9A Introduction to Equations - an expression is numbers, operations and pronumerals without an equals sign, whereas an equation is a statement saying two things are equal. They have a LHS and RHS (either side of = sign) What makes an equation true is a solution. - 9B Inspection to solve equations - inspecting the equation/expression to see what the pronumeral may be to make a solution. - 9C Equivalent Equations - means both sides of the equals sign are equal (e.g. 2 + x = 5 (x being 3)) - 9D Solving Equations systematically - using backwards BODMAS (SAMDOB) to find the value of the pronumeral - 9E Equations with fractions - to solve an equation that has a fraction on one side, multiply both sides by the denominator. If it is not just a fraction on one side, manipulate the equation. x/3 + 5 = 8, minus 5 to make x/3 = 3, then times by three to get x = 9. - 9F Equations with Brackets - collect like terms and expand brackets. - 9G Formulas & Relationships - The subject of an equation is the pronumeral by itself on the LHS. A formula or rule is an equation that contains two or more pronumerals, one of them the subject of the equation. - 9H Using Equations to Solve Problems - define pronumerals, write and systematically solve the equation. Make sure you have included the answer to the question. Include the necessary units (e.g. cm, L, etc.) Measurement Ex 10B to 10J, 7.5 & 7.6 - 10B Using and converting units of length - When converting to smaller, multiply to power of ten, and when converting to larger measurement, divide by power of ten. - 10D Pi and Circumference of Circles - Diameter (distance across the middle of circle), Radius (distance centre to circle), Chord (line interval connecting two points on a circle), Tangent is a line that touches the circle at a point (at right angle to radius). A sector is a portion of a circle enclosed by two radii and a portion of the circle. A segment is an area of the circle cut off by a chord. Circumference (c) is the distance around a circle. C = 2 (pi) r or C = (pi) d - 10E Arc Length and Perimeter of sectors and composite figures - Circular arc’s (l) angle is theta (θ), at the centre of the circle. ARC LENGTH - l = θ over 360 x 2 (pi) r or l = θ over 360 x (pi) d, PERIMETER - p = θ over 360 x 2 (pi) r + 2r - 10F Units of Area - 1mm², 1cm² (100mm²), 1m² (10000cm²), 1ha (1mh x 1hm)(10000m²), 1km² (1000000m²), Rectangle - length (l) x breadth (b) = area (A), Square - A = s x s, A = s² (s is side of square) - 10G Area of a triangle - ½ b x h = ½ bh = bh over 2 - 10H Area of parallelograms - A = b (base) x h (perpendicular height) - 10I areas of composite shapes - find the area through adding or subtracting other shapes from the main shape. - 7.5 Volume of a Prism - written in cubic units, Volume of rectangular prism V = lbh, Volume of cube = s³, Volume of triangular prism A=½ bh V = Ah (h=height of prism) - 7.6 Volume and Capacity - Volume is a space inside a 3D shape. Capacity - the amount of liquid the volume can hold. 1mL = 1cm³, 1L = 1000cm³, 1kL = 1000 L = 1m³ - 10J Mass and Temperature - 1L of water has a mass of 1 kg and 4 degrees. 1 cm³ of water weighs 1g. 1kg = 1000g, 1g = 1000mg, 1t = 1000kg