Robinson Tuition20 mixed questions from 8 Year 8 topics, 53 marks. It covers percentages and percentage change to probability, the last third of the year in the order schools usually teach it.
Type your answers below for an instant mark and a score, or print the sheet, mark it with the answers sheet, and use the solutions to see every step written out. Set one a week and watch the score climb.
A spinner can land on red, blue, green or yellow.
The table shows the probabilities for three of the colours.
| Colour | red | blue | green | yellow |
|---|---|---|---|---|
| Probability | 0.2 | 0.35 | 0.1 |
Work out the probability that the spinner lands on yellow.
Probabilities add up to 1
| 0.2 + 0.35 + 0.1 | = | 0.65 |
| P(yellow) | = | 1 - 0.65 |
| P(yellow) | = | 0.35 |
0.35
The stem and leaf diagram shows the number of press-ups 11 students did in one minute.
| Stem | Leaves |
|---|---|
| 0 | 6 8 |
| 1 | 1 3 5 7 9 |
| 2 | 2 4 6 8 |
Key: 1 | 1 = 11 press-ups
a)
11 values, so median is the 6th
| (11 + 1) ÷ 2 | = | 6 |
6, 8, 11, 13, 15, 17
17
b)
| Range | = | 28 - 6 |
| Range | = | 22 |
22
A house is worth £240 000. Its value increases by 4% each year.
Work out the value of the house after 3 years. Give your answer to the nearest pound.
multiplier for +4% is 1.04
3 years, so multiply by 1.04 three times
| 1.043 | = | 1.124864 |
| 240000 × 1.124864 | = | 269967.36 |
nearest pound
£269 967
The scatter graph shows the outside temperature, in °C, and the number of portions of soup sold by a cafe on each of 8 days.
a)
Trend: soup sales fall as temperature rises
(11, 10) is far below the trend
(11, 10)
b)
Line of best fit, ignoring (11, 10)
Go up from 9 °C to the line
Go across to the portions axis
Reading: about 46 or 47
About 47 portions (accept 44 to 50)
Year 8 grew 30 sunflowers. The table shows information about their heights, h cm.
| Height (h cm) | Frequency |
|---|---|
| 0 < h ≤ 50 | 3 |
| 50 < h ≤ 100 | 7 |
| 100 < h ≤ 150 | 12 |
| 150 < h ≤ 200 | 8 |
a) highest frequency is 12
100 < h ≤ 150
b) median is between the 15th and 16th
| 3 + 7 | = | 10 |
| 10 + 12 | = | 22 |
100 < h ≤ 150
c) midpoint × frequency
| 25 × 3 | = | 75 |
| 75 × 7 | = | 525 |
| 125 × 12 | = | 1500 |
| 175 × 8 | = | 1400 |
| total | = | 3500 |
| 3500 ÷ 30 | = | 116.66... |
116.7 cm
The mean of 8 numbers is 12.
The mean of 5 of these numbers is 9.
Work out the mean of the other 3 numbers.
| Total of 8 | = | 8 × 12 |
| Total of 8 | = | 96 |
| Total of 5 | = | 5 × 9 |
| Total of 5 | = | 45 |
| Total of 3 | = | 96 - 45 |
| Total of 3 | = | 51 |
| Mean | = | 51 ÷ 3 |
| Mean | = | 17 |
17
Triangle ABC is similar to triangle PQR.
AB corresponds to PQ, and BC corresponds to QR.
AB = 6 cm, PQ = 9 cm and BC = 8 cm.
Work out the length of QR.
| Scale factor | = | PQ ÷ AB |
| Scale factor | = | 9 ÷ 6 |
| Scale factor | = | 1.5 |
| QR | = | BC × 1.5 |
| QR | = | 8 × 1.5 |
| QR | = | 12 |
12 cm
A skate ramp is made of concrete. It is a triangular prism. The cross-section is a right-angled triangle with base 3 m and height 1.2 m. The ramp is 2.5 m wide.
Concrete costs £95 per m3.
Work out the cost of the concrete for the ramp.
area of cross-section
| A | = | 12 × 3 × 1.2 |
| A | = | 1.8 m2 |
| V | = | 1.8 × 2.5 |
| V | = | 4.5 m3 |
| 4.5 × 95 | = | 427.50 |
£427.50
Lena says, "If two triangles have the same three angles, they must be congruent."
a)
SSS, SAS, ASA, RHS
b)
Same angles = same shape, but not always the same size
e.g. sides 3, 4, 5 and sides 6, 8, 10 have equal angles
AAA only shows the triangles are similar
The table shows the shoe sizes of the students in a year group.
| Shoe size | Frequency |
|---|---|
| 4 | 5 |
| 5 | 9 |
| 6 | 12 |
| 7 | 8 |
| 8 | 6 |
a)
Mode = size with the highest frequency
Highest frequency is 12
6
b)
Add the frequencies
| Total | = | 5 + 9 + 12 + 8 + 6 |
| Total | = | 40 |
40
c)
Sizes 7 and 8
| 8 + 6 | = | 14 |
14
The ratio of a distance in miles to the same distance in kilometres is 5 : 8.
a) miles : km = 5 : 8
| 40 ÷ 5 | = | 8 |
| 8 × 8 | = | 64 |
64 km
b)
| 12 ÷ 8 | = | 1.5 |
| 5 × 1.5 | = | 7.5 |
7.5 miles
Write down whether each type of data is discrete or continuous.
counted = discrete, measured = continuous
a) counted
discrete
b) measured
continuous
c) measured
continuous
d) counted
discrete
Rectangle A measures 4 cm by 6 cm.
Rectangle B is mathematically similar to rectangle A. The shorter side of rectangle B is 10 cm.
a)
| scale factor | = | 10 ÷ 4 |
| scale factor | = | 2.5 |
2.5
b)
| longer side | = | 6 × 2.5 |
| longer side | = | 15 |
15 cm
Work out 30% of 60% of £250
| 60% of £250 | = | 0.6 × 250 |
| 60% of £250 | = | £150 |
| 30% of £150 | = | 0.3 × 150 |
| 30% of £150 | = | £45 |
£45
a) 100% + 12% = 112%
| 280 × 1.12 | = | 313.60 |
£313.60
b) 100% - 30% = 70%
| 75 × 0.7 | = | 52.50 |
£52.50
a) 2 triangles + 3 rectangles
triangular prism
b) a cuboid has 3 pairs of faces
given: one 3 by 2, one 1 by 2, two 3 by 1
missing: a 1 by 2 face and a 3 by 2 face
1 by 2 goes on the right of the 3 by 2 face
3 by 2 goes on top of the top 3 by 1 face
net complete: 6 faces
A shop sells two sizes of box of teabags.
Small box: 80 teabags for £2.40
Large box: 240 teabags for £6.60
Which box is the better value for money? Show your working.
Cost of one teabag
| Small: 240p ÷ 80 | = | 3p |
| Large: 660p ÷ 240 | = | 2.75p |
2.75p < 3p
Large box: 2.75p per teabag, not 3p
The diagram shows angle ABC.
Using a ruler and compasses only, construct the bisector of angle ABC.
You must show all your construction lines.
Then use a protractor to measure one of the two angles your bisector makes.
Compass point on B: one arc crossing both arms
Same radius from each crossing point: arcs cross inside the angle
Join B to where the arcs cross
76° ÷ 2 = 38°
Bisector drawn, each half 38°
Here is a sketch of an equilateral triangle with sides of 6 cm.
Using a ruler and compasses only, construct the triangle accurately in the space below. You must show all your construction arcs.
Write down the size of each angle in your triangle.
Draw AB = 6 cm
Compasses set to 6 cm
Arc from A, arc from B: they cross at C
Join AC and BC
180° ÷ 3 = 60°
Each angle is 60°
ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
A = {multiples of 3} B = {even numbers}
Complete the Venn diagram.
| A | = | {3, 6, 9, 12} |
| B | = | {2, 4, 6, 8, 10, 12} |
A and B) In both sets
6, 12
A only) In A but not B
3, 9
B only) In B but not A
2, 4, 8, 10
outside) The numbers left over
1, 5, 7, 11
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.