NSAA 2021 Mathematics S1

• A.$\frac{1}{125x^7y^2}$
• B.$\frac{1}{125x^6y^2}$
• C.$\frac{1}{25x^5y}$
• D.$\frac{1}{25x^4y}$
• E.$\frac{1}{5x^3}$
• F.$\frac{1}{5x^2}$
• G.$\frac{y}{x^2}$
• H.$5xy^2$

Answer: E

• A.$\frac{7x-1}{4x-1}$
• B.$\frac{7x-2}{4x-1}$
• C.$\frac{7x+1}{4x+1}$
• D.$\frac{7x+2}{4x+1}$
• E.$\frac{9x-1}{4x-1}$
• F.$\frac{9x-2}{4x-1}$
• G.$\frac{9x+1}{4x+1}$
• H.$\frac{9x+2}{4x+1}$

Answer: B

• A.$q = \frac{2r}{24-3pr}$
• B.$q = \frac{3r}{2r-p}$
• C.$q = \frac{6r}{4-p}$
• D.$q = \frac{6r}{8-pr}$
• E.$q = \frac{r-2}{12p}$
• F.$q = \frac{3r-6}{4p}$
• G.$q = \frac{pr-8}{12p}$
• H.$q = \frac{3pr-24}{4p}$

Answer: D

• A.$3y + 4x = 25$
• B.$3y - 4x = 25$
• C.$3y - 4x = -7$
• D.$3y - 4x = 7$
• E.$4y + 3x = 24$
• F.$4y - 3x = 24$
• G.$3y + 4x = 24$
• H.$3y - 4x = 24$

Answer: A

Two solid cylinders, P and Q, are shown, where $x > y$.

Cylinder P has diameter $x$ and height $y$.

Cylinder Q has diameter $y$ and height $x$.

What is the positive difference between the total surface areas of P and Q?

• A.0
• B.$\frac{\pi}{4}(x^2 - y^2)$
• C.$\frac{\pi}{2}(x^2 - y^2)$
• D.$\pi(x^2 - y^2)$
• E.$2\pi(x^2 - y^2)$
• F.$\frac{\pi}{4}xy(x-y)$
• G.$\pi xy(x-y)$

Answer: C

• A.-4
• B.-3
• C.-2
• D.$- \frac{3}{2}$
• E.$- \frac{2}{3}$
• F.$- \frac{1}{2}$
• G.$- \frac{1}{3}$
• H.$- \frac{1}{4}$

Answer: E

The price of item P is reduced by 10%. The next day, the new price is increased by 10%.

The price of item Q is increased by 10%. The next day, the new price is reduced by 10%.

How does the final price of each item compare to the original price of that item?

• A.item P final price: lower than original, item Q final price: lower than original
• B.item P final price: lower than original, item Q final price: higher than original
• C.item P final price: higher than original, item Q final price: lower than original
• D.item P final price: higher than original, item Q final price: higher than original
• E.item P final price: the same as original, item Q final price: the same as original

Answer: A

• A.218
• B.219
• C.220
• D.221
• E.222
• F.223
• G.224
• H.225

Answer: F

[diagram not to scale]

SQT is a right-angled triangle with the right angle at Q.

The point R is on SQ such that SR : RQ = 1:3

QRP is a right-angled triangle with the right angle at Q.

PR = ST = 8 cm

QT = 4 cm

What is the length of PQ, in cm?

• A.$2\sqrt{3}$
• B.$4\sqrt{3}$
• C.$\sqrt{19}$
• D.$\sqrt{37}$
• E.$\sqrt{55}$
• F.$\sqrt{61}$

Answer: D

• A.£0.50
• B.£2.00
• C.£2.25
• D.£3.00
• E.£4.50
• F.£6.75

Answer: E

• A.-43
• B.-12
• C.-2
• D.0
• E.2
• F.12
• G.43

Answer: F

An online company sells storage containers.

The following items are available:

A customer orders two containers at random from those available.

What is the probability that the two containers will have a combined capacity of exactly 10 litres?

• A.$\frac{7}{25}$
• B.$\frac{14}{25}$
• C.$\frac{7}{45}$
• D.$\frac{14}{45}$
• E.$\frac{7}{50}$

Answer: D

• A.$- \frac{\sqrt{3}}{9}$
• B.$-5\sqrt{2}+10$
• C.$3\sqrt{3}-8$
• D.$6\sqrt{3}-10$
• E.$14\sqrt{2}-20$
• F.$15\sqrt{3}-26$
• G.$21\sqrt{3}-38$

Answer: F

$P, Q$ and $R$ are points on the circumference of a circle with centre $O$ as shown in the diagram.

[diagram not to scale]

Angle $PQR = 140^{\circ}$

$PR = 7$ cm

Which of the following expressions gives the radius of the circle, in cm?

• A.$7 \sin{10^{\circ}}$
• B.$3.5 \sin{55^{\circ}}$
• C.$3.5 \sin{70^{\circ}}$
• D.$7 \sin{55^{\circ}}$
• E.$\frac{3.5}{\sin{40^{\circ}}}$
• F.$\frac{7}{\sin{80^{\circ}}}$
• G.$\frac{3.5}{\sin{20^{\circ}}}$
• H.$\frac{7}{\sin{40^{\circ}}}$

Answer: E

• A.$\frac{2}{27}$
• B.$\frac{1}{12}$
• C.$\frac{1}{9}$
• D.$\frac{4}{27}$
• E.$\frac{1}{6}$
• F.$\frac{1}{4}$
• G.$\frac{7}{12}$

Answer: B

The following right-angled triangles have the same hypotenuse length.

[diagram not to scale]

Which of the following is a correct expression for $y$ in terms of $x$?

• A.$y = \sqrt{2}x$
• B.$y = \frac{\sqrt{2}x}{2}$
• C.$y = \frac{\sqrt{2}x}{3}$
• D.$y = \frac{\sqrt{2}x}{6}$
• E.$y = \sqrt{6}x$
• F.$y = \frac{\sqrt{6}x}{2}$
• G.$y = \frac{\sqrt{6}x}{3}$
• H.$y = \frac{\sqrt{6}x}{6}$

Answer: G

The greatest diagonal distance between the two vertices of a cuboid, as shown in the diagram, is $\sqrt{77}$ cm.

A similar cuboid has all its lengths exactly half the lengths of the original cuboid.

The sides of this smaller cuboid are 2 cm, 3 cm and $x$ cm.

What is the value of $x$, in cm?

• A.$\frac{5}{2}$
• B.5
• C.$\frac{5\sqrt{2}}{2}$
• D.$5\sqrt{2}$
• E.$\frac{\sqrt{102}}{2}$
• F.$\sqrt{102}$

Answer: A

• A.9.6
• B.14
• C.24
• D.25
• E.28
• F.50
• G.56

Answer: F

• A.$100fmpx$
• B.$\frac{100fmp}{x}$
• C.$\frac{100mpx}{f}$
• D.$\frac{100mp}{fx}$
• E.$\frac{fmpx}{100}$
• F.$\frac{fmp}{100x}$
• G.$\frac{mpx}{100f}$
• H.$\frac{mp}{100fx}$

Answer: H

• A.0
• B.1
• C.2
• D.3
• E.4
• F.5
• G.infinitely many

Answer: F