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SECTION A [40 MARKS]
1. (a) Using prime factorization, find √2704.
……….……………………………… [2]
(b) Find the HCF and LCM of 500𝑥 2 and 675𝑥 3 .
HCF = …………...…...… and LCM = ……………………….. [3]
2. Evaluate each of the following without using a calculator.
(a)
(−2550)×[−43−(−43)]
122 −√144
…...…...…………………………….. [2]
(b)
(−9)2 × 7 + [(−21) ÷ 3] − (−8)
…………………………………….. [1]
3. By using a suitable approximation, estimate the value of
(70.42)2 × 2.983
√398.721
.
…………………………………….. [2]
19-20_MYE_SEC1ACC_MATHS_QP
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4. Find the ratio of 324 seconds to 10 minutes.
………………………………… [1]
5. The angles that measure (9𝑚)° and (18𝑝)° are supplementary. Find the value of (𝑚 + 2𝑝)°.
………………………………….…° [2]
6. In the diagram below, the straight line LO is parallel to the straight line PQ. ∆YXZ is a right-angled
triangle, ∠𝑋𝑌𝑍 = 47° and ∠𝑋𝑌𝑄 = 41°. Find the values of the angles c and d.
NOT TO SCALE
c = …………………… ° and d = …..……………… ° [4]
19-20_MYE_SEC1ACC_MATHS_QP
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7. A car has a constant speed of x km/h.
The distance travelled by the car is 28 km in 18 minutes 40 seconds.
Find the value of x.
x = ……………………..………….… [2]
8. In the diagram below, CDEG is a parallelogram. Given that ∠𝐶𝐺𝐹 = 58°, ∠𝐶𝐹𝐸 = 𝑥°,
∠𝐹𝐸𝐷 = (𝑥 + 13)° and ∠𝐹𝐶𝐺 = 𝑦°. Find the values of x° and of y°.
NOT TO SCALE
x = ………………… ° and y = ………………… ° [3]
19-20_MYE_SEC1ACC_MATHS_QP
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9. Construct and label the quadrilateral 𝐴𝐵𝐶𝐷 such that 𝐴𝐵 = 7 cm, 𝐵𝐶 = 5.5 cm, 𝐶𝐷 = 10 cm,
∠𝐷𝐴𝐵 = 130° and ∠𝐴𝐵𝐶 = 75°.
[3]
(i) Measure and write down the length of AD.
……………………………………….. cm [1]
(ii) Write down the measure of ∠𝐶𝐷𝐴.
…………………………………………. ° [1]
10. The length of a side of a square is 8.23 m, correct to 3 significant figures.
(i)
Find the lower bound for the perimeter of the square.
……………………………………….. cm [1]
(ii)
Find the upper bound for the area of the square, correct to 3 decimal places.
……………..………………………..cm2 [1]
19-20_MYE_SEC1ACC_MATHS_QP
6
11. On a year-end sale, Suzy and Marie bought the same designer bag marked at $365. Suzy bought hers
on the first day of the sale and got a discount of 15%. However, Marie got a further discount of 20% on
the original discounted price because she bought hers on the last day of the sale. Calculate the difference
between the marked price and the price that Marie paid for the designer bag, expressing your answer in
2 decimal places.
…………………………..…………… [3]
12. A chicken meal costs $2 more than a spaghetti meal. Mrs. Tan’s money is just enough to buy 6 orders
of chicken meal or 12 orders of spaghetti meal. She wishes to buy equal number of orders of chicken
and spaghetti meals. If $x represents the cost of a spaghetti meal, formulate an equation in x and find
the number of orders of each meal she can buy with her money.
…………………………..…………… [3]
19-20_MYE_SEC1ACC_MATHS_QP
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4
13. Callista, Kyra and Rae run around an oval track. They took 15 hours, 0.3 hours and x min to complete
one lap, respectively. Suppose they started to run at the same time, same starting lane and same
direction. If they all meet at the starting point again after 2 hours and 24 minutes ,
(i) find the time, in x minutes, in which Rae completed one lap, such that 9 < x < 15.
…………………………..…………… min [3]
(ii) hence, find the total number of laps the three people have completed after 2 hours and 24 minutes.
…………………………..…………. laps [2]
19-20_MYE_SEC1ACC_MATHS_QP
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SECTION B [60 MARKS]
1. (a) Solve the equation 2(4𝑑 – 1) – 6(𝑑 + 7) = −29
………….……………………………. [2]
(b) Solve the inequality 8 − 5𝑦 ≤ 20 − 2𝑦.
…....………………………………….. [2]
(c) Find the smallest prime number value of y based on the solution in part 1(b) above.
y = .………………………………….. [1]
2. In 2018, the value of a house is $x. In 2019, the value of the house depreciates by 18%.
If the value of the house in 2019 is $37 392, calculate the value of the house in 2018.
$ ....………………………………….. [2]
19-20_MYE_SEC1ACC_MATHS_QP
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3. (a) The general term of a sequence is Tn = 5n + k, where k is a constant.
Given that 𝑇23 of the sequence is 121, find the the value of k.
k = ……….………………………….. [2]
(b) Consider the sequence 5, 2, –1, –4 , –7, …
(i) Write down a general formula for the nth term.
𝑇𝑛 = ..………………………………… [1]
(ii) If the kth term is –70, find the value of k.
k = ...………………………………… [2]
19-20_MYE_SEC1ACC_MATHS_QP
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4. In the diagram, the straight lines 𝐴𝐵𝐶 and 𝐸𝐹𝐺𝐻 are parallel. Given, 𝐵𝐷 = 𝐷𝐹, ∠𝐵𝐹𝐷 = 55° and
∠𝐶𝐵𝐺 = 62°. Calculate
NOT TO SCALE
(i) ∠𝐵𝐷𝐹,
.……………………………………. ° [1]
(ii) ∠𝐹𝐺𝐷,
.……………………………………. ° [1]
(iii) ∠𝐷𝐹𝐺.
.……………………………………. ° [2]
(iv) Hence, the ratio of the angles of ∆𝐹𝐷𝐺 can be written in the form of 4 : p : q where p < q. Find
the values of p and q.
p = ....…………… q = ………………… [2]
19-20_MYE_SEC1ACC_MATHS_QP
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5. (a) Written as a product of their prime factors,
1st integer :
2nd integer :
3𝑎 × 5 × 72
33 × 5𝑏 × 7𝑐
The two integers have an HCF of 315 and an LCM of 33075.
Find the value of a, b and c.
a =…………… b = …………… and c = ……………. [4]
(b) Hence, find the values of the 1st and 2nd integers.
1st integer = …………………. 2nd integer = ………………... [2]
(c) If the product of the 1st integer and d is a perfect cube, find the lowest value of d such that d is
a positive integer.
d = .……………..………………... [2]
19-20_MYE_SEC1ACC_MATHS_QP
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6. In the diagram, 𝑃𝑄 is parallel to 𝑆𝑇.
If ∠𝑃𝑄𝑅 = 97° and ∠𝑄𝑅𝑆 = 124°, calculate the acute angle ∠𝑅𝑆𝑇.
NOT TO SCALE
∠𝑅𝑆𝑇 = ………………..……………. [2]
7. ∆𝐷𝐸𝐹 is an equilateral triangle.
If EFG is a straight line and ∠FDG = 40°, find the values of w and s.
NOT TO SCALE
w = ……………° and s = …………….° [2]}
19-20_MYE_SEC1ACC_MATHS_QP
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8. Felix uses two different wires, A and B, to form a rhombus and a rectangle. He bent wire A into a
rhombus with perimeter (4x + 28)cm and wire B into a rectangle. The longer side of the rectangle is
six times the side of the rhombus whilst the shorter side of the rectangle is only two times the side of
the rhombus. Felix used the whole length of the two wires without cutting off any edges to make the
shapes. Express the perimeter of wire B in terms of x.
………………………………….. cm [2]
9. A man invested $ 5800 in a business stock that pays simple interest at a rate of 3% per annum. Find
the time taken for his investment to grow to $8236.
..……………………………... years [2]
10. A farmer plans to create a square shaped area with side length of 42m, to hold his animals. He
wants to minimize on the building cost, and so decides to re-use all of the existing length of
fence that presently holds his animals. The present fenced-up area is a rectangle, with breadth of
(12 + 2y)m and length which twice its breadth. Calculate the value of y.
y = ……………..………………..… [4]
19-20_MYE_SEC1ACC_MATHS_QP
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11. The pie chart shows Felicia’s monthly expenditure.
NOT TO SCALE
(i) Calculate the value of y°.
y = …..………………..…………….° [2]
(ii) Hence, find the percentage of the amount spent in food.
…..………………..……………. % [1]
(iii) If Felicia cares for all her monthly expenditure using her monthly salary of $3250, find the
amount she spends just for transportation.
$ .…..………………..……………. [2]
19-20_MYE_SEC1ACC_MATHS_QP
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12. The figure shows an 8-sided irregular polygon. Find the value of x°.
NOT TO SCALE
x = ..………………..…………….° [3]
13. Nicole was 15p years old in 2017. Her younger sister, Chloe was born when Nicole was 9p years
old. If the sum of both of their ages five years from now is 56, find the value of p.
p = ….………………..………….. [4]
19-20_MYE_SEC1ACC_MATHS_QP
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14. Using a straight edge, connect the points X, Y and Z below and identify the polygon that will be
formed.
……………….…………………….. [1]
(i)
Measure and write down the size of each angle.
∠YXZ = ………………. ° , ∠XYZ = ………………. ° , ∠XZY = ………………. ° [3]
(ii)
Construct the perpendicular bisector of line segments XZ and YZ.
[3]
(iii)
Label the intersection of these bisectors as point P.
(iv)
Draw a line passing through point P that is parallel to the longest side of the triangle.
[1]
[2]
END OF EXAM
19-20_MYE_SEC1ACC_MATHS_QP