Year 7 Math Test
Time allowed: 90 minutes +5 minutes reading questions
Try best to answer the questions as much as you can.
Marks may be deducted for careless or badly arranged work.
The diagrams are not to scale.
Calculator is NOT allowed.
PART A – Foundation (35 marks)
1. Convert these mixed numbers to improper fractions in simplest form. (2 marks)
6
a) 8
15
28
b) −3
42
2. Convert these improper fractions to mixed numbers in simplest form. (2 marks)
28
a)
10
−40
b)
15
3. Compare fractions:
(4 marks)
3
7
−3 ¿
4
4. Calculate: (4 marks)
1 3
a) 8 +6
2 5
3 2
b) 6 −3
20 3
1 2 3
c) 3 +1 −2
2 3 4
5. Calculate: (3 marks)
3 1
a) of 5
4 3
8
b) 120% of
3
1 3
c) 1 of
2 8
6. Calculate: (4 marks)
3 3
a) 9 ÷ 3
7 4
2 1
b) 7 ÷ 1
3 6
7. Express these percentages as mixed numbers in their simplest form. (4 marks)
a) 316%
b) 235%
c) 488%
8. Convert these fractions to percentages, (3 marks)
3
a)
8
3
b) 1
20
36
c) −2
40
9. Match the questions with their correct answer. (5 marks)
Questions Answers
10% of $200 $8
20% of $120 $16
10% of $80 $20
50% of $60 $24
20% of $200 $25
5% of $500 $30
30% of $310 $40
10% of $160 $44
1% of $6000 $60
50% of $88 $93
10. Convert the following decimals to fractions in their simplest form.
a) 10.15
b) 9.075
c) 18.12
11.
PART B – Development (45 marks)
1.
2. All the rows, columns and main diagonals in the magic square multiply to give 216. Find the
missing numbers. (3 marks)
3. Find the value of a in these diagram (4 marks)
4. Two roads merge into a freeway at the same angle, as shown. Find the size of the obtuse angle,
a ° , between the parallel roads and the freeway. (3 marks)
5. Find the smallest composite number that has the five smallest prime numbers as factors.
(4 marks)
6. Of 20 students, 10 play sport and 12 play a musical instrument, with some of these students
playing both sport and music. Two students do not play any sport or musical instrument.
What percentage of the students play a musical instrument but not sport? (5 marks)
7. Place the following values in order from highest to lowest:
86 % , 0.5 % , 0.6 , 0.125 , 22 % , 75 % , 2 % , 0.78 (6 marks)
8. Yakob has asked his friends what their favourite school subject is, and he has created the
following divided bar graph from the information.
Redraw these results as a pie chart. (4 marks)
9. The mirror line on the grid is at a 45° angle. Draw the reflected image. (6 marks)
10. A number is doubled, then 3 is added and the result is doubled again. This gives a result of 34 .
Set up and solve an equation to find the original number, showing all the steps clearly.
(6 marks)
PART C – Challenge (20 marks)
1. Using whole numbers and any of the four operations (+, −, ×, ÷), describe how you would obtain
the ‘Finish’ number from the ‘Start’ number in the following table. Your rule must work for every
pair of numbers in its table. (4 marks)
2. Find the value of a in the diagram. To help find the solution, you might need to draw additional
parallel lines in the diagram. (5 marks)
3. Solve each of the equation: 2(3 x +4 )+5 (6 x+ 7)+ 8(9 x +10)=123 (5 marks)
4. Find the values of a and b for each of the geometric figure. (6 marks)
