3NA_WA 3 Revision WS

Math Response

(1) Write 250 000 in standard form.

Type answer here

Correct Answer: 2.5\times10^5

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Math Response

(2) Write 0.000184 in standard form.

Type answer here

Correct Answer: 1.84\times10^{-4}

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Math Response

(4) In the diagram, $$\angle ABC=90\degree$$ , AB = 12 cm, BC = 5 cm and AC = 13 cm. Write down as a fraction, the value of $$\tan\angle BAC$$ .

Type answer here

Correct Answer: \frac{5}{12}

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Fill in the Blanks

Math Response

(7) Given that the equation of a line is $$3y+6x=5,$$ find the

value of k if $$\left(1,k\right)$$ lies on the line.

Type answer here

Correct Answer: -\frac{1}{3}

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Math Response

(9) The coordinates of two points A and B are $$\left(-6,5\right)$$ and $$\left(7,-2\right)$$ . Find the equation of the line AB.

Type answer here

Correct Answer: y=-\frac{7}{13}x+\frac{23}{13}

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Fill in the Blanks

Open Ended

(11) In the diagram, a 10 m ladder XZ is leaning against the top of a wall. James lowers the ladder to B and the ladder is 2 m further away from the foot of the wall. Assuming that the ladder collapses if the angle between the ladder and the ground is less than $$40\degree$$ , determine whether the ladder will collapse after James adjusted the ladder. Show your working clearly.

Math Response

(12) Find the equation of the line passing through $$\left(8,-2\right)$$ with gradient $$-\frac{1}{4}$$ .

Type answer here

Correct Answer: y=-\frac{1}{4}x

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Math Response

(13) The population of San Marino and the world population in 2020 were 34017 and 7.75 billion respectively. Find the population of San Marino as a percentage of the world population. Give your answer in standard form, correct to 2 significant figures.

_____%

Type answer here

Correct Answer: 4.4\times10^{-4}

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Open Ended

(15) The length of the line segment, AB is $$\sqrt[]{80}$$ units. Given further that point C is $$\sqrt[]{260}$$ units from point A and $$\sqrt[]{180}$$ units from B, show that triangle ABC is a right-angled triangle.

Math Response

(18) A line passes through A(– 2 , 1) and B(– 7 , –10). Find the gradient of AB.

gradient = _______

Type answer here

Correct Answer: \frac{11}{5}

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Math Response

(19) In the diagram, $$\angle ABC=90\degree$$ , AB = 12 cm, BC = 5 cm and AC = 13 cm. Write down, as a fraction, the value of $$\sin\angle ACB$$ .

Type answer here

Correct Answer: \frac{12}{13}

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Math Response

(20) In the diagram, $$\angle ABC=90\degree$$ , AB = 12 cm, BC = 5 cm and AC = 13 cm. Write down, as a fraction, the value of $$\cos\angle BAC$$ .

Type answer here

Correct Answer: \frac{12}{13}

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Math Response

(21) In the diagram, ABC is a straight line. $$\angle ABD=\angle ADC=90\degree$$ , AD = 10 cm and BD = 8 cm. Calculate angle DAB.

______ $$\degree$$

Type answer here

Correct Answer: 53.1

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Math Response

(21) In the diagram, ABC is a straight line. $$\angle ABD=\angle ADC=90\degree$$ , AD = 10 cm and BD = 8 cm. Calculate the length of BC.

______ cm

Type answer here

Correct Answer: 10.7

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Multiple Select

(23) Given that $$\sin x\degree=0.623$$ , find the possible value(s) of x for $$0\degree<x<180\degree$$ . Correct your answer to 1 dp.

________ $$\degree$$

• $$38.5\degree$$

• $$51.5\degree$$

• $$128.5\degree$$

• $$141.5\degree$$

Multiple Choice

(24) Given that $$\cos x\degree=-0.791$$ , find the possible value(s) of x for $$0\degree<x<180\degree$$ . Correct your answer to 1 dp.

________ $$\degree$$

• $$37.7\degree$$

• $$52.3\degree$$

• $$127.7\degree$$

• $$142.3\degree$$

Math Response

(25) QRN is a right-angled triangle where QN = 6 cm and NR = 8 cm. PQN is a straight line. Expressing your answer as a fraction in its simplest form, find $$\tan\angle QRN$$ .

Type answer here

Correct Answer: \frac{3}{4}

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Math Response

(26) QRN is a right-angled triangle where QN = 6 cm and NR = 8 cm. PQN is a straight line. Expressing your answer as a fraction in its simplest form, find $$\cos\angle PQR$$ .

Type answer here

Correct Answer: -\frac{3}{5}

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Math Response

(27) QRN is a right-angled triangle where QN = 6 cm and NR = 8 cm. PQN is a straight line. Expressing your answer as a fraction in its simplest form, find $$\sin\angle PQR$$ .

Type answer here

Correct Answer: \frac{4}{5}

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​END OF WA 3 REVISION