2018 Carnival Assignment

Mr.A.Isaac

Answer ALL questions

1. (a) (Fractions and Approximation) Determine the EXACT value of:

(i) ( 5 2

4+ 5

2

5 ) ÷ ( 2 3

4 − 5

2

5 )

(ii) 2315! − 2.71344 + .3560

giving your answer correct to 2 significant figures and 2 decimal places.

(iii) Write the number 0.000059384567 AND 43 in standard form.

(b) A credit union pays 10% per annum compound interest on all fixed deposits. A customer

deposited $24 000 in an account. Calculate the TOTAL amount of money in the account at the end of two years.

(c) John deposited $2000 into Republic Bank at a rate of 10% for 2 years. Calculate his interest. (d) Jane deposited $2000 into Republic Bank and the money grew to $12, 000 at a rate of 20%.

How long did her deposit take to reach that amount?

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Mr.A.Isaac

2. (a) (Substitution) Given that 𝒂 = −𝟏,𝒃 = −𝟐 𝑎𝑛𝑑 𝒄 = −𝟑, find the value of: (i) 𝑎 − 𝑏 + 𝑐

(ii) 𝑎! − 𝑐! − (2𝑎𝑏)!

(iii) −2𝑎𝑏𝑐

(b) (Simplify) the following: (i) −8𝑥𝑦! − 3𝑎𝑏! − 13𝑥𝑦! + 9𝑎𝑏!

(ii) −5𝑥 2𝑥 − 3𝑦 + 4𝑥 + 𝑦

(iii) 9𝑥!! × 3𝑥!!

(iv) !!!!!

!!!! × (2𝑥6) (v) 6 𝑎 − 𝑏 − 2(3𝑎 − 4𝑏)

(c) (Binary Operation) An operation is defined by 𝒂 ∗ 𝒃 = 2𝑎 − 3𝑏

Calculate the exact value of (i) 2 ∗ 3 (ii) (2 ∗ 3) ∗ −4

(d) (Factorize) completely: (i) 49𝑦! − 625

(ii) 2𝑏𝑥 − 2𝑏𝑦 − 𝑡𝑥 + 𝑡𝑦

(iii) 𝑝𝑥 + 𝑝𝑦 − 𝑞𝑥 − 𝑞𝑦

(iv) 4 (x+3) + m (x+3)

(v) x (x−1) − 5 (x−1)

(vi) 2x2 −5x−3

(vii) 6x2 +17x+12

(viii) (a+c)2−4

(ix) 16−(b+3)2

(e) Solve the pair of (simultaneous equations): −2𝑥 + 6𝑦 = 4 4𝑥 − 𝑦 = 3

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Mr.A.Isaac

3. (Algebra Fraction): Simplify the following: (i) (!!!)

!− (!!!!)

! (ii) !

(!!!)− !

(!!!!)

(Expansion/Expanding brackets): Expand the following below: (i) (2𝑥 − 5)! (ii) (2𝑥 + 4)(3𝑥 − 5)

Solve the following using factorization and quadratic formula - !!± !!!!!"

!!

(i) 2𝑥! + 5𝑥 − 7 = 0

Solving (Simultaneous equations) Quadratic linear systems

(i) 𝑦 = 𝑥 − 6

𝑥! + 𝑦! = 26

(ii) 𝑦 = 𝑥! − 𝑥 − 18

𝑦 = 𝑥 − 3

Worded problems involving simultaneous equations (i) Suppose you bought supplies for a party. Three rolls of ribbons and 5 party hats cost $8.

Later, you bought 2 rolls of ribbons and 4 party hats for $6. (a) Write a pair of simultaneous equation representing the information given above. (b) Solve the pair of simultaneous equations

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Mr.A.Isaac

4. (a) A school of 90 students in form 5.

54 students study Physical Education. 42 students study Music 6 students study neither Physical Education nor Music. x students study both Physical Education and Music.

(i) Copy and complete the Venn diagram below to represent the given information above.

(ii) Write an expression, in x, to represent the TOTAL number of tourist in the survey.

(iii) Write an equation, in x, to represent the TOTAL number of tourist in the survey.

(iv) Calculate the value of x.

(v) How many students studied physical Education ONLY?

(vi) How many students studied Music ONLY?

(vii) How many students studied both Physical Education and Music?

(viii) List all the subsets of P

P M

U

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Mr.A.Isaac

5. (a) Given 𝑓 𝑥 = 2𝑥! − 5𝑥 − 3 𝑓𝑜𝑟 − 1 ≤ 𝑥 ≤ 4, complete the following table below

𝑥 -1 0 1 2 3 4

𝑓(𝑥)

(b) Using 2cm to represent 1 unit on the 𝒙 𝒂𝒙𝒊𝒔 and 1 cm to represent 1 unit on the

𝒚 𝒂𝒙𝒊𝒔, plot the points whose x and y values are recorded in your table, and draw a smooth curve through the points.

(c) Use your graph, estimate the value of y when 𝑥 = 2. Show on your graph how the value

was obtained. (d) Using the same graph, draw the graph y = 4, for −1 ≤ 𝑥 ≤ 4. (e) Without further calculations,

(i) State the y intercept (ii) Estimate the minimum value of the function y (iii) State the minimum point (iv) State the values of x of the equation: 𝑥! − 2𝑥 − 3 = 0 (v) State the values of 𝑥 for 𝑥! − 2𝑥 − 3 = 4

(f) List the members of the domain (g) List the members of the range (h) List the set of ordered pairs

(i) Draw an arrowed diagram

End of Assignment