Download Grade 10 Mathematics Assessment Paper 1

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Grade 10 Mathematics
Assessment
Paper 1
Use of a calculator is not allowed.
All numerical answers must be given exactly.
1. Consider the numbers
7
2.31
√
12
From these five numbers, write down
(a) an irrational number,
Answer ……………………………………….[1 mark]
(b) a prime number,
Answer ……………………………………….[1 mark]
(c) all integers.
Answer ……………………………………….[1 mark]
2. (a) List all six factors of 18.
Answer ……………………………………….[2 marks]
(b) Find the highest common factor of 72 and 60.
Answer ……………………………………….[2 marks]
3. Calculate
(
)
Answer ……………………………………….[3 marks]
4. Find the value of
(a)
Answer ……………………………………….[1 mark]
(b)
Answer ……………………………………….[1 mark]
5. Simplify (give the answer in the form
, where a and b are integers).
(a)
Answer ……………………………………….[2 marks]
(b) (
)
Answer ……………………………………….[3 marks]
6. Let
and
(a) Write x as a decimal.
.
Answer ……………………………………….[1 mark]
(b) Write y in standard form (i.e.
, where
and b is an integer).
Answer ……………………………………….[1 mark]
(c) Calculate the product xy and give the answer in standard form.
Answer …………………………………….. [2 marks]
7. Expand and simplify.
(a) (
)
(
)
Answer …………………………………….. [2 marks]
(b) (
)(
)
Answer ……………………………………….. [2 marks]
8. Solve the inequality and illustrate the solution on the number line.
(
)
(
)
Answer ……………………………………….. [3 marks]
9. Solve the simultaneous equations
Answer
and
.
x = ………………………
y =………………………. [4 marks]
10.
EG is a diameter
of the circle through
E, C and G.
The tangent AEB
is parallel to CD
and angle AEC = 68°.
Calculate the size of the following angles.
(a) Angle CEG
Answer ………………………………………….. [1 mark]
(b) Angle ECG
Answer ………………………………………….. [1 mark]
(c) Angle CGE
Answer ………………………………………….. [1 mark]
(d) Angle ECD
Answer ………………………………………….. [1 mark]
Name: ……………………………………………………………………………...
Paper 2
Use of a calculator is required.
Unless otherwise stated in the question, all numerical answers must be given exactly or to three
significant figures.
11. (a) Bruce mixes blue and yellow paint to make green paint.
He uses blue and yellow paint in the ratio
blue : yellow = 7 : 3.
(i) He makes 15 litres of green paint.
How many litres of yellow paint does he use?
Answer ……………………………………….. [2 marks]
(ii) He buys the yellow paint in tins. Each tin contains 2 litres of paint.
Write down the number of tins of yellow paint he buys.
Answer ……………………………………….. [1 mark]
(b) Tins of red paint cost $9.25 each.
In a sale, the shop reduces the price by 12%.
Calculate the sale price of one tin of red paint.
Answer ……………………………………….. [2 marks]
(c) The price of a tin of yellow paint has changed from $8 to $9.
By what percentage has the price changed?
Answer ……………………………………….. [2 marks]
12. Adam thought of a number, a, and Betty thought of a number, b.
(a) Adam multiplied his number by 5 and Betty multiplied her number by 2, then they added their
results and the sum was 11.
Write an equation in a and b, which represents the information above.
Answer ……………………………………….. [1 mark]
(b) If Adam multiplies his number by 17 and Betty multiplies her number by 7, then the sum of their
results is 32.
Write an equation in a and b, which represents the information above.
Answer ……………………………………….. [1 mark]
(c) Find the numbers Adam and Betty thought.
Answer a = …………………… b = ………………….. [3 marks]
13. The diagram below shows a regular seven-sided polygon and a square. The polygons share one of
the sides.
y°
y
(a) Each of the interior angles measures x°.
One of the angles is marked in the diagram.
Calculate the value of x, giving your answer correct to 1 decimal place.
Show all your working.
Answer …………………………………………….. [4 marks]
(b) Find the measure of the angle y°.
Answer …………………………………………….. [2 marks]
(c) Find the number of sides of a regular polygon, of which each interior angle has measure 168°.
Show all your working.
Answer …………………………………………….. [4 marks]
14. Quadrilateral BCDE is cyclic.
O is the centre of the circle.
Line BF is tangent to the circle at point B.
E
D
110°
50°
6
NOT TO SCALE
F
O
C
A
B
(a) Find the measure of
(i) angle EBC
Answer ……………………………………….. [2 mark]
(ii) angle BCD
Answer ……………………………………….. [1 mark]
(iii) angle FBC (the angle between the tangent line and the side BC)
Answer ……………………………………….. [1 mark]
Triangle ABE is inscribed in a semicircle.
The length of the side AE is 6.
The radius of the circle is 6.
(b) Calculate the length of the chord AB.
Answer ……………………………………….. [3 marks]
(c) Find the measure of the angle AED. Show all your working.
Answer ……………………………………….. [3 marks]
15. (a) Is the triangle in the diagram right-angled?
Give the reason.
4 cm
10 cm
12 cm
NOT TO SCALE
Answer ……………………………………….. [3 marks]
(b) The formula for the area, A, of a triangle is
,
Where a is a side of a triangle and h is the height dropped on side a.
Given that the area of the triangle in the diagram above is 18.7 cm2 (correct to 1 d.p.), find the length
of the shortest height of the triangle.
Answer ……………………………………….. [3 marks]