AlgebraIB MYP Maths Standard: Topic test

1. 1
   Let $m=4$ and $n=-3$.

   (a)

   What is the value of $2m^{2}-n^{3}$?

   [1 mark]

   • A$5$
   • B$59$
   • C$91$
   • D$-59$

   (b)

   Which expression is $(x+4)(x-3)$ when expanded and simplified?

   [1 mark]

   • A$x^{2}-12$
   • B$x^{2}+7x-12$
   • C$x^{2}-x-12$
   • D$x^{2}+x-12$

   (c)

   Expand and simplify $3(2x-1)-2(x-4)$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Ana is factorising expressions for her homework.

   (a)

   Which is the factorised form of $x^{2}-81$?

   [1 mark]

   • A$(x-9)(x+9)$
   • B$(x-9)^{2}$
   • C$x(x-81)$
   • D$(x-3)(x+27)$

   (b)

   Which is the factorised form of $x^{2}-7x+12$?

   [1 mark]

   • A$(x+3)(x+4)$
   • B$(x-2)(x-6)$
   • C$(x-3)(x-4)$
   • D$(x-1)(x-12)$

   (c)

   Factorise fully $6y^{2}-15y$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A tile designer in Seoul makes isosceles triangular tiles. Each of the two equal sides is $(3x+2)$ cm long and the base is $(x+8)$ cm long.

   (a)

   A tile has a perimeter of $54$ cm. Form an equation in $x$ and solve it to find $x$.

   [3 marks]

   (b)

   The designer needs the perimeter to be less than $66$ cm, and $x$ must be a whole number. Write and solve an inequality, and state the largest possible value of $x$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   In physics, the kinetic energy $E$ joules of an object of mass $m$ kg moving at speed $v$ m/s is given by $E=\frac{1}{2}mv^{2}$.

   (a)

   (i) Rearrange the formula to make $v$ the subject. (ii) An object of mass $8$ kg has kinetic energy $900$ J. Find its speed. (iii) Explain why only the positive square root is used in part (ii).

   [6 marks]

   (b)

   A different object has kinetic energy $360$ J when moving at $6$ m/s. (i) Rearrange the formula to make $m$ the subject. (ii) Find the mass of the object. (iii) The speed of the object doubles and its mass does not change. Find the new kinetic energy and explain what happens to the kinetic energy.

   [6 marks]

   Total for question 4: 12 marks

5. 5
   Samira solves quadratic equations by factorising, by the quadratic formula and by using the discriminant.

   (a)

   Which pair of values are the solutions of $x^{2}-2x-15=0$?

   [1 mark]

   • A$x=-5$ and $x=3$
   • B$x=5$ and $x=3$
   • C$x=5$ and $x=-3$
   • D$x=-5$ and $x=-3$

   (b)

   How many real solutions does $2x^{2}+x+3=0$ have?

   [1 mark]

   • ANone
   • BOne
   • CTwo
   • DInfinitely many

   (c)

   Use the quadratic formula to solve $x^{2}+4x-3=0$. Give both solutions to $2$ decimal places.

   [2 marks]

   Total for question 5: 4 marks

6. 6
   At a market stall in Istanbul, $3$ apples and $2$ oranges cost $12$ lira, and $1$ apple and $2$ oranges cost $8$ lira.

   (a)

   What is the price of one apple?

   [1 mark]

   • A$1$ lira
   • B$3$ lira
   • C$4$ lira
   • D$2$ lira

   (b)

   What is the total cost of $5$ apples and $5$ oranges?

   [1 mark]

   • A$20$ lira
   • B$25$ lira
   • C$30$ lira
   • D$40$ lira

   (c)

   Let $a$ be the price of one apple and $o$ the price of one orange, in lira. Using the answer to part (a), form and solve an equation to find the price of one orange.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   A photographer in Seoul prints rectangular photos. A photo has width $x$ cm and length $(x+7)$ cm.

   (a)

   One photo has an area of $60$ cm$^2$. Form a quadratic equation and solve it to find the width of the photo.

   [3 marks]

   (b)

   Another photo is also $x$ cm wide and $(x+7)$ cm long, but its area is $100$ cm$^2$. Use the quadratic formula to find its width to $1$ decimal place, and explain which solution you use.

   [4 marks]

   Total for question 7: 7 marks

8. 8
   A school in Kuala Lumpur sells tickets for its annual concert. Adult tickets cost RM $15$ and student tickets cost RM $8$. On Friday, $120$ tickets were sold for a total of RM $1\,240$.

   (a)

   Let $a$ be the number of adult tickets and $s$ the number of student tickets sold on Friday. Write down two equations, solve them to find $a$ and $s$, and check your answer.

   [6 marks]

   (b)

   On Saturday, $50$ adult tickets are sold and the school wants to raise at least RM $1\,500$ that day. The hall has $150$ seats. (i) Find the least number of student tickets that must be sold. (ii) Decide whether the target can be reached, and give a reason.

   [6 marks]

   Total for question 8: 12 marks

End of questions