2024 Year 10 Assessment Task 1
Mathematics Stage 5 (Core and Standard Paths)
Ms Prithika & Mr Salim
General
Instructions
• Working time – 45 minutes
• Write using black or blue pen
• Sketches may be made in pencil
• NESA approved calculators are allowed in this task
• For Questions 1–2, show relevant mathematical reasoning
and/or calculations
• A reference sheet is provided at the back of this paper
• Write your full name and class in the spaces provided
below
Total marks:
30
Short/Extended Answer Questions (pages 3–8)
• Attempt All questions
• Allow about 45 minutes
Student name:
_______________________________________
Class:
_________
Mark: ___________ / 30
Blank page
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Short/Extended Answer Questions
30 marks
Attempt All Questions
Allow about 45 minutes for these questions
•
Answer the questions in the spaces provided. These spaces provide guidance
for the expected length of response.
•
Your responses should include relevant mathematical reasoning and/or calculations.
Question 1. Write the following in index form:
a)
1
4× 𝒂 × 𝒂 × 𝟒 × 𝒂 × 𝟒 × 𝟒 × 𝒂 × 𝒂
Answer: 𝟒𝟑 × 𝒂𝟓
b) Express the following with positive indices: 5 𝒎−𝟑 𝒏𝟐
Answer: 5
𝑛2
1
𝑚3
Question 2.
(a)
Solve the equation:
−𝟐𝟒 + 𝟕𝒙 = −𝟑
2
Answer: 𝟕𝒙 = −𝟑 + 𝟐𝟒
𝟕𝒙 = −𝟐𝟏
𝒙 = −𝟑
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(b) Write an equation and solve the equation to find 𝒙.
1
i) If 4 is added to 𝒙, the result is 6
Answer: 𝒙 + 𝟒 = 𝟔
𝒙=𝟔=𝟒
𝒙=𝟐
2
ii) If 𝒙 is divided by 3 and then 2 is added, the result is 8
Answer:
𝒙
𝟑
+𝟐=𝟖
𝒙
𝟑
𝒙
𝟑
=𝟖−𝟐
=𝟔
𝒙=𝟔×𝟑
𝒙 = 𝟏𝟖
(c)
Solve the following equation by first expanding the bracket then collecting the like terms.
𝟒(𝟐𝒙 − 𝟏) + 𝟐(𝟐𝒙 − 𝟑) = −𝟐𝟐
Answer: 𝟖𝒙 − 𝟒 + 𝟒𝒙 − 𝟔 = −𝟐𝟐
𝟏𝟐𝒙 = −𝟐𝟐 + 𝟏𝟎
𝟏𝟐𝒙 = −𝟏𝟐
𝒙 = −𝟏
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2
Question 3. Simplify the following by factorising it first.
a)
𝟑𝒙𝟐 +𝟔𝒙
𝒙+𝟐
Answer: a)
𝟑𝒙(𝒙+𝟐)
2+2
𝟏𝟐𝒙−𝟒
b)
𝟑𝒙−𝟏
b)
(𝒙+𝟐)
=𝟑𝒙
(𝟑𝒙−𝟏)
=4
Question 4. Simplify the following expression:
Answer:
𝟒(𝟑𝒙−𝟏)
3(𝑥+4)
×
10
𝟑(𝒙+𝟒)
𝟏𝟎
÷
𝟔(𝒙+𝟒)
2
𝟏𝟓
15
6(𝑥+4)
3
=
4
Question 5: Simplify the following algebraic expression:
𝟐𝒙+𝟏
𝟓
Answer:
−
𝒙−𝟐
𝟑
𝟑(𝟐𝒙+𝟏)−𝟓(𝒙−𝟐)
𝟏𝟓
=
=
3
𝟔𝒙+𝟑=𝟓𝒙+𝟏𝟎
𝟏𝟓
𝒙+𝟏𝟑
𝟏𝟓
-5-
Question 6. Write an equation for the information on the diagram shown below. Then solve it to
3
find the value of 𝑥.
Answer: 𝟐(𝟐𝒙 + 𝟒) + 𝟐 × 𝟐 = 𝟐𝟐
𝟒𝒙 + 𝟖 + 𝟒 = 𝟐𝟐
𝟒𝒙 = 𝟐𝟐 = 𝟏𝟐
𝒙 = 𝟏𝟎
Question 7. Use an inequality to describe the solution represented on the lines below.
a)
Answer:
1
b)
1
Answer
2
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Question 8. Solve the following inequalities and represent the solution on a number line.
𝟏
𝟐
2
𝒙≤𝟔
Answer:
Qu Question 9. Solve the following inequalities:
3
𝒂−𝟑
𝟐
≤ −𝟏
Answer :
Question 10. Solve the simultaneous equations using the substitution method.
𝒚 = 𝟒𝒙 + 𝟏------(1)
𝟐𝒙 − 𝟑𝒚 = −𝟐𝟑------(2)
Answer :
From equation (2)
Put 𝒙 = 𝟐, into equation (1)
Therefore (𝒙, 𝒚) = (𝟐, 𝟗)
𝟐𝒙 = 𝟑(𝟒𝒙 + 𝟏) = −𝟐𝟑
𝟐𝒙 − 𝟏𝟐𝒙 − 𝟑 = −𝟐𝟑
−𝟏𝟎𝒙 = −𝟐𝟑 + 𝟑
−𝟏𝟎𝒙 = −𝟐𝟎
𝒙=𝟐
𝒚 = 𝟒𝒙 + 𝟏
𝒚 =𝟒×𝟐+𝟏
𝒚=𝟗
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Reference Sheet
Area of Square= 𝒙 × 𝒙
Area of Rectangle = 𝒍 × 𝒃
Index Law
am × an = am+n
am ÷ an = am−n
1
a−m = m
a
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