AISAAC-FORM4MATHEMATICS-ASSIGNMENT#1 Show all working

Answer ALL questions

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

(i) ( 2 3

4 − 5

2

5 ) ÷ ( 2 3

4 − 5

2

5 )

(ii) 24.5! − 2.8935 + 20

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

(iii) Write the number 0.00009384567 AND 432190 in standard form. (Consumer Arithmetic)

(b) BDS$ means Barbados dollars and EC$ means Eastern Caribbean dollars.

(i) Karen exchanged BDS $2000.00 and received EC $2700.00. Calculate the value of one BDS$ in $EC$.

(ii) If Karen exchanged EC $432.00 for BDS$, calculate the amount of BD$$ which Karen would receive.

[Assume that the buying and selling rates are the same.] (c) A credit union pays 8% 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.

(d) John deposited $2000 into Republic Bank at a rate of 5% for 3 years. Calculate his interest. (e) Jane deposited $10000 into Republic Bank and the money grew to $12, 000 at a rate of 2%.

How long did her deposit take to reach that amount?

AISAAC-FORM4MATHEMATICS-ASSIGNMENT#1 Show all working 2

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

(iv) +2𝑎𝑏𝑐 (v) 𝑎 − 𝑏 + 2𝑐𝑏

(vi) 2𝑎𝑏 − 𝑎𝑏 + 𝑐

(vii) 6𝑎 − 𝑏 + 4𝑐

(viii) (𝑎 − 𝑏)! + 2𝑐!

(ix) 𝑎! − 𝑏! − 𝑐!

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

(ii) −5𝑥 2𝑥 − 3𝑦 + 4𝑥 + 𝑦

(iii) 9𝑥!! × 3𝑥!!

(iv) !!!!!

!!!! × (2𝑥6) (v) (2𝑥!)!

(vi) 3 𝑥 + 𝑦 − 4𝑥

(vii) 6 𝑎 − 𝑏 − 2(3𝑎 − 4𝑏)

(viii) −4 (2𝑐 − 3𝑎 − 4𝑏)

(ix) 3𝑎!𝑏 − 5𝑏! − 8𝑐! + 4𝑎!𝑏

(c) (Binary Operation) An operation is defined by 𝒂 ∗ 𝒃 = 3𝑎𝑏𝑐 − 2𝑎𝑏 + 𝑏!.

Calculate the exact value of (i) 2 ∗ 3 (ii) 4 ∗−1 (iii) −5 ∗−2 (iv) 0 * 5 (v) (2 ∗ 3) ∗ −4

(d) (Factorize) completely: (i) 36𝑦! − 625

(ii) 2𝑏𝑥 − 2𝑏𝑦 − 𝑡𝑥 + 𝑡𝑦

(iii) 𝑝𝑥 + 𝑝𝑦 − 𝑞𝑧 − 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): (i) −2𝑥 − 𝑦 = −3 −𝑥 − 2𝑦 = −3

(ii). −2𝑥 + 6𝑦 = 4 4𝑥 − 𝑦 = 3

AISAAC-FORM4MATHEMATICS-ASSIGNMENT#1 Show all working 3

3. (Algebra Fraction):

Simplify the following: (i) (!!!)

!− (!!!!)

! (ii) !!!!

!+ !!!!

! (iii) !

(!!!)+ !

(!!!!)

(Expansion/Expanding brackets): Expand the following below: (i) (2𝑥 − 5)! (ii) (2𝑥 + 4)(3𝑥 − 5) (iii) (4𝑥 − 2)(5𝑥 − 6)

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

!!

(i) 2𝑥! + 5𝑥 − 7 = 0 (ii) 2𝑦! + 5𝑥 − 3 = 0 (iii) 𝑥! + 2𝑥 − 3 = 0 (iv) 2𝑥! + 7𝑥 + 3 = 0 (v) 𝑡! − 2𝑡 − 3 = 0

Solving (Simultaneous equations) Quadratic linear systems

(i) 𝑦 = 𝑥 − 6

𝑥! + 𝑦! = 26

(ii) 𝑦 = 𝑥! − 𝑥 − 18

𝑦 = 𝑥 − 3

(iii) 𝑦 = 𝑥! − 𝑥 − 2

𝑦 = −𝑥 + 2

(iv) 𝑦 = −2𝑥 + 3

𝑦 = 𝑥! − 6𝑥 + 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

AISAAC-FORM4MATHEMATICS-ASSIGNMENT#1 Show all working 4

Completing the square

(i) Put in 𝟐𝒙𝟐 + 𝟐𝟎𝒙+ 𝟑 = 𝟎, in the form of 𝒂 𝒙+ 𝒉 𝟐 + 𝒌.

(ii) State the axis of symmetry

(iii) State the minimum/maximum point

(iv) State the turning point

(v) State the y intercept

(vi) Sketch the graph for 𝑎(𝑥 + ℎ)! + 𝑘 = 0

(vii) Using your answer from part (i) solve for the value of x for 𝑎(𝑥 + ℎ)! + 𝑘 = 0

AISAAC-FORM4MATHEMATICS-ASSIGNMENT#1 Show all working 5

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

(ix) List all the subsets of M

(x) List all the subsets of U

P M

U

AISAAC-FORM4MATHEMATICS-ASSIGNMENT#1 Show all working 6

4. T and E are subset of a universal set, U, such that: U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 } T = ( multiple of 3 } E = { Even numbers }

(i) Draw a Venn diagram to represent this information. (ii) List the members of the set

T ∩ 𝐸 (𝑇 ∪ 𝐸) ⁄ only T only E T E

(iii) What is the number of elements in n(T) n(E) n(T ∩ E) n(T∩E) ⁄ n(only T) n(only E) n (𝑈)

(IV) (a) List all the subsets of T. (b) List all the subsets of E.

5. S and T are subsets of a Universal set U such that: U = { k, l, m, n, p, q, r } S = { k, l, m, p } T = {k, p, q }

(i) Draw a Venn diagram to represent this information. (ii) List , using set notation, the members of the set

(a) S ∪ 𝑇 (b) S⁄

End of Assignment