Test 6 - Pearson Test 6 - Pearson

Form 3 Mathematics TestTest 7: Pythagorean theorem andtrigonometric ratiosTotal: 50 marksName: ________________________________________ Date: __________________________Section AWrite down the correct letter for each of the following questions.1. In triangle ABC, C = 90°. Which one of the following statements is true?A AB 2 = BC 2 – AC 2BB BC 2 = AB 2 – AC 2C AB 2 = BC 2 – AC 2D AC 2 = BC 2 + AC 2AC2. In triangle PQR, P = 90°, PQ = 5.7 cm and PR = 9.1 cm. The length of QR,correct to two decimal places, equals:A10.74 cmQBC7.09 cm14.80 cm5.7 cmD. 10.73P9.1 cmR3. Which one of the following statements is true for triangle PRS?ABPS is the adjacent side of PPS is the opposite side of PRCRS is the adjacent side of PDPR is the adjacent side of SPS1/7Maths TestPearson Botswana. Permission is given to photocopy these pages for school use.

4. In triangle STR, R = 90°. Which one of the following trigonometric ratiosis correct?Acos T = SR/STTBtan S = SR/TRCDsin S = ST/TRsin T = SR/STSR5. In triangle PQR, Q = 90°, PQ = 4.5 cm, QR = 2.2 cm, and PR = 5.01 cm.Cos P =A 1.113B 0.898C 0.489D 0.439P4.5 cm Q2.2 cm5.01 cmR6. Which one of the following statements is true for triangle KDR?A sin K = cos KB sin 2 K = cos 2 KC sin 2 K + cos 2 K = 1D sin 2 K + cos 2 K = tan 2 KKDR7. Which one of the following statements is true?A If P increases from 0° to 90°, then cos P increases from 0 to 1.B If P increases from 0° to 90°, then sin P increases from 0 to 1.C If P increases from 0° to 90°, then tan P increases from 0 to 1.D If P increases from 0° to 90°, then tan P decreases from 1 to 0.2/7Maths TestPearson Botswana. Permission is given to photocopy these pages for school use.

8. Which one of the following statements is true?A If P increases from 0° to 90°, then tan P decreases from 0 to 1.B If P increases from 0° to 90°, then cos P increases from 0 to 1.C If P increases from 0° to 90°, then sin P decreases from 1 to 0.D If P increases from 0° to 90°, then cos P decreases from 1 to 0.9. Which one of the following statements is true?A If P increases from 0° to 90°, then tan P increases from 0 to infinity.B If P increases from 0° to 90°, then cos P increases from 0 to 1.C If P increases from 0° to 90°, then sin P decreases from 1 to 0.D If P increases from 0° to 90°, then tan P decreases from infinity to 0.10. Which one of the following statements is true?ABAC =4.7 cmD= tanP37°aSSection B11. In triangle TRS, S = 90°, RS = 3.4 cm and TS = 5.8 cm.R3.4 cmT5.8 cmS3/7Maths TestPearson Botswana. Permission is given to photocopy these pages for school use.

a) Write down the Pythagorean Theorem for ∆TRS. (2)b) Substitute the given values in the formula. (2)c) Calculate the length of RT correct to two decimal places. (2)____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________12. In triangle PQR, R = 90°, PR = 4 cm, PQ = 7.3 cm.P4 cm7.3 cmRQa) Write down the Pythagorean Theorem for ∆PQR. (2)b) Substitute the given values in the formula. (2)c) Calculate the length of RQ correct to two decimal places. (2)____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________4/7Maths TestPearson Botswana. Permission is given to photocopy these pages for school use.

13. In triangle ABC, C = 90°, BC = 2 cm, AC = cm, and AB = 4.5 cm.B4.5 cm2xAxCa) Write down the Pythagorean Theorem for ∆ABC. (2)b) Substitute the given values in the formula. (2)c) Calculate the value for correct to two decimal places. (2)d) Write down the lengths of (2)(i)(ii)AC, andBC correct to two decimal places._____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________5/7Maths TestPearson Botswana. Permission is given to photocopy these pages for school use.

14. In triangle PQR, , , and represent the lengths of QR, PR and PQrespectively. Write down in terms of , and :QrpPqRa) sin P (1)b) cos P (1)c) tan P (1)d) sin Q (1)_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________15. In triangle XYZ, Z = 90°, X = 23°, and XZ = 7.5 cm.YX23°7.5 cm Za) Write, down with reasons, the size of Y. (2)6/7Maths TestPearson Botswana. Permission is given to photocopy these pages for school use.

Calculate, correct to two decimal places, the lengths of:b) YZ (3)c) XY (3)__________________________________________________________________________________________________________________________________________________________________________16. In triangle MNO, M = 90°, MO = 7.5 cm, and NO = 9 cm.N9 cmM7.5 cmOa) Write down the value of cos O correct to three decimal places (1)Calculate:b) the size of O (3)c) the size of N (2)d) the length of MN correct to two decimal places. (2)Total: 507/7Maths TestPearson Botswana. Permission is given to photocopy these pages for school use.

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