Robinson Tuition20 mixed questions from 9 Year 8 topics, 50 marks. It covers compound measures to angles in polygons, the second third of the year in the order schools usually teach it.
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A straight line passes through the points (1, 7) and (3, 13).
Find the equation of the line.
Give your answer in the form y = mx + c
Gradient
| change in y | = | 13 - 7 | ||
| = | 6 | |||
| change in x | = | 3 - 1 | ||
| = | 2 | |||
| m | = | change in ychange in x | ||
| m | = | 62 | ||
| m | = | 3 | ||
| Substitute (1, 7) into y = 3x + c | ||||
| 7 | = | 3 × 1 + c | ||
| 7 | = | 3 + c | ||
| -3 | c | = | 4 | -3 |
| Check with (3, 13) | ||||
| 3 × 3 + 4 | = | 13 | ||
y = 3x + 4
Show each inequality on its number line.
Solid circle = included (≤ or ≥), open circle = not included (< or >)
a)
Solid circle at -2
Arrow to the right
Solid circle at -2, arrow right
b)
Open circle at -1
Solid circle at 4
Join them
Open circle at -1 to solid circle at 4
A model of a car is made to a scale of 1 : 24.
Real = 24 × model
a)
18 × 24 = 432 cm
432 ÷ 100 = 4.32
4.32 m
b)
1.44 m = 144 cm
144 ÷ 24 = 6
6 cm
The diagram shows two parallel lines crossed by a straight line.
One of the marked angles is 71°. The angle marked x° is the co-interior angle between the parallel lines on the same side of the crossing line.
Work out the value of x. Give a reason for your answer.
Co-interior angles add to 180°
| x + 71 | = | 180 | ||
| -71 | x | = | 109 | -71 |
x = 109
Co-interior angles add up to 180°
A pattern of shapes tessellates if the shapes fit together around every point with no gaps and no overlaps.
a) hexagon
| 360 ÷ 6 | = | 60 |
| 180 - 60 | = | 120 |
| 3 × 120 | = | 360 |
3 hexagons make 360° exactly
b) pentagon
| 360 ÷ 5 | = | 72 |
| 180 - 72 | = | 108 |
| 3 × 108 | = | 324 |
| 4 × 108 | = | 432 |
324° leaves a gap, 432° overlaps
c) octagon angle = 135°, square = 90°
| 135 + 135 + 90 | = | 360 |
360° so no gaps
Here are the first four terms of an arithmetic sequence.
7 12 17 22
Explain why 81 is not a term of this sequence.
7, 12, 17, 22, 27, 32, ...
Terms go up in 5s
Every term ends in 2 or 7
81 ends in 1
Or use the nth term 5n + 2
| 5n + 2 | = | 81 | ||
| -2 | 5n | = | 79 | -2 |
| ÷5 | n | = | 15.8 | ÷5 |
15.8 is not a whole number
Every term ends in 2 or 7, and 81 ends in 1
A is the point with coordinates (2, 4).
B is the point with coordinates (8, 10).
Work out the coordinates of the midpoint of AB.
Midpoint: mean of each coordinate
| x | = | 2 + 82 |
| x | = | 102 |
| x | = | 5 |
| y | = | 4 + 102 |
| y | = | 142 |
| y | = | 7 |
(5, 7)
The diagram shows the speedometer of a car.
a) Each small mark = 10 mph
Halfway between 60 and 80
70 mph
b)
70 ÷ 5 = 14
14 × 8 = 112
112 km/h
The diagram shows an inequality on a number line.
Write down the inequality shown, using x.
Solid circle at -1: included
| x | ≥ | -1 |
| Open circle at 4: not included | ||
| x | < | 4 |
Put them together
-1 ≤ x < 4
The diagrams show a triangle and a quadrilateral.
a) angles in a triangle add to 180°
| 52 + 73 | = | 125 |
| x | = | 180 - 125 |
x = 55°
b) angles in a quadrilateral add to 360°
| 84 + 108 + 77 | = | 269 |
| y | = | 360 - 269 |
y = 91°
DE and FG are parallel straight lines.
Triangle ABC is drawn so that A lies on DE, and B and C both lie on FG.
D is to the left of A and E is to the right of A.
Angle DAB = 48° and angle ACB = 63°.
Work out the size of angle BAC.
Give a reason for each stage of your working.
| ABC | = | DAB |
| ABC | = | 48° |
| Alternate angles are equal | ||
| BAC | = | 180° - 48° - 63° |
| BAC | = | 69° |
Angles in a triangle add to 180°
69°
A, B and C are three vertices of a parallelogram ABCD.
A is (−4, −1), B is (1, −1) and C is (3, 3).
a)
A (-4, -1), B (1, -1), C (3, 3)
A, B and C plotted
b)
DC is parallel to AB and the same length
A to B: 5 right, 0 up
so D to C: 5 right, 0 up
D = (3 - 5, 3 - 0)
D (-2, 3)
Simplify
a)
a2 terms: 5a2 - 2a2 = 3a2
a terms: 3a + 4a = 7a
3a2 + 7a - 9
b)
yx is the same as xy
4xy + 2xy = 6xy
-7 + 10 = 3
6xy + 3
Two angles fit together on a straight line. One of the angles is 64° and the other angle is y°.
a)
| y + 64 | = | 180 | ||
| -64 | y | = | 116 | -64 |
y = 116
b)
Angles on a straight line add up to 180°
Here are four pieces of algebra.
A: 3x + 2 = 11 B: A = lw C: 4y − 7 D: 2(x + 3) ≡ 2x + 6
Write down which one is
a)
expression: no equals sign
C
b)
equation: true for one value (x = 3)
A
c)
formula: works out one quantity from others
B
d)
identity: true for every x, the ≡ sign
D
Here are the first four terms of an arithmetic sequence.
5 9 13 17
Find an expression, in terms of n, for the nth term of the sequence.
5, 9, 13, 17
Common difference = +4
4n: 4, 8, 12, 16
Each term is 1 more than 4n
| nth term | = | 4n + 1 |
| Check n = 3 | ||
| 4 × 3 + 1 | = | 13 |
4n + 1
Solve w4 + 2 = 9
| w4 + 2 | = | 9 | ||
| -2 | w4 | = | 7 | -2 |
| ×4 | w | = | 28 | ×4 |
w = 28
Dan and Ella share 45 sweets.
Ella gets 7 more sweets than Dan.
Dan says, "I got 20 sweets."
Is Dan right? You must show how you get your answer.
Dan = d, Ella = d + 7
| d + d + 7 | = | 45 | ||
| 2d + 7 | = | 45 | ||
| -7 | 2d | = | 38 | -7 |
| ÷2 | d | = | 19 | ÷2 |
| Check | ||||
| 19 + 26 | = | 45 | ||
No, Dan got 19 sweets, not 20
A straight line has equation y = 3x − 2
Compare with y = mx + c
y = 3x - 2
a)
| m | = | 3 |
3
b)
| c | = | -2 |
Crosses the y-axis where x = 0
(0, -2)
a)
7 × 2 - 3 = 11
11 × 2 - 3 = 19
19 × 2 - 3 = 35
7, 11, 19, 35
b) - 8 each time
50, 42, 34, 26, 18
Answer the questions above and your score appears here.
Every question here is original and written by Robinson Tuition, drawn from the Year 8 topic worksheets. It follows the Key Stage 3 programme of study.