Coordinates and Graphs Questions and Answers - Form 1 Topical Mathematics

Share via Whatsapp

Questions

  1. Find the angle θ in degrees from the figure below
    coordinates q1
  2. In the diagram below, determine the equation of the line XY in the form y = mx + c
    Coordinates q2
  3. Find the equation of a line which passes through the point (2, 3) and is perpendicular to y – 3x+ 1 = 0, giving your answer in the form y = mx + c
  4. T is the mid-point of line XY where X is point (1,4) and Y is the point (-5, 10). Find the equation of a line, L2 which is perpendicular to line XY and goes through point T
  5.  
    1. On the grid provided below, plot points A(2,1) B(-4,3) and C(2,5)
    2. Given that the gradient of CD = -1 and CD =AD locate D and complete the quadrilateral ABCD
    3. What name is given to quadrilateral ABCD?
  6.  In the figure below (not drawn to scale), PQRS is a rectangle and P and Q are the points (3, 2) and (1,4) respectively.
    Coordinates q6
    Given that the equation of the line PQ is y =3x -7, find:
    1. The equation of line QR
    2. The coordinates of point R
    3. The coordinates of point S
  7. OABC is a trapezium such that the coordinates of O, A , B and C are (0, 0), (2, -1), (4, 3) and (0, y)
    1. Find the value of y
    2. M is the mid-point of AB and N is the mid-point of OM. Find in column form
      1. the vector AN
      2. the vector 
      3. Vector AC NC
    3. Hence show that A, N and C are collinear
  8. Use ruler and a pair of compasses only in this question.
    1. Construct triangle ABC in which AB = 7 cm, BC = 8 cm and ∠ABC = 600.
    2. Measure
      1. side AC
      2. ∠ ACB
    3. Construct a circle passing through the three points A, B and C. Measure the radius of the circle.
    4. Construct ∆ PBC such that P is on the same side of BC as point A and ∠ PCB = ½ ∠ ACB, ∠ BPC = ∠ BAC measure ∠ PBC.
  9. ABCD is a parallelogram with vertices A (1,1) and C(8,10). AB has the equation 4x -5y = -1 and BC has the equation 5x – 2y = 20. Determine by calculation;
    1.  the co-ordinates of the point M where the diagonals meet
    2. The co-ordinates of the vertices B and D
    3. the length of AB correct to 4 significant figures
  10. The table shows corresponding values of x and y for a certain curve; 
     x  1.0  1.2  1.4  1.6  1.8  2.0  2.3
     y  6.5  6.2  5.2  4.3  4.0  2.6  2.4

    Using 3 strips and mid-ordinate rule estimate the area between the curve, x-axis

Answers

  1. 2x - 3y + 6 =0
    -3y = -2x – 6
    y = 2x/3 + 2
    When y = 0 x = -3
    x = 0 y = 2

    Co-ordinate of y – intercept is (0,2) 
    Coordinate of x – intercept is (-3,0)
    ∴ ∠CAO = tan-1 2/3
    = 33.69o
    ∴∠θ = 180 – 33.69o
    = 146.31o
    coordinates answer 1
  2. Point y(4 + -2/2, 7 + -1/2) = (1, 3)
    grad AB = 7 + 1/4 + 2 = 8/6
    grad xy = - ¾
    grad xy = - ¾
    y – 3/x – 2 = - ¾
    y = - ¾ x + 15/4
  3.  Y = 3x – 1
    M =3
    M1M2 = -1
    M2 = -1/3
    y – 3/x -2= -1/3
    3y – 9 =-x +2
    3y/3 = -x/3 + 11/3
    Y = -x/3 + 11/3
  4.  Pt T is 1 + 5/2, 4 + 10/2 = (-2, 7)
    grad. of grid xy = 10 - 4/-5 -1 = 14/-6 = -7/-3
    ∴ grad of L2 = 3/7
    Take a general pt P(x,y) on L2
    y - 7/x - 2 = 3/7
    →7y – 49 = 3x + 6
    7y = 3x + 55
    Or y = 3x + 55 (equation of L2
  5.  a, b
    coordinates answer 5ab
    (c) Name : a kite
    1. Grad of line QP = 4-2/1-3= 2/-2= -1
      Grad of line QR = 1
      Take a pt Q(1,4) and T(x,y) on line QR
      y- 4/x – 1= 1
      y – 4 = x -1
      y = x + 3 .....equ. of QR
    2. y= x+3 …(i) Equ of QR
      y = 3x -7 ...(ii) Equ. of Pr
      Solving simultaneously ;:
      x +3 = 3x -7
      2x = 10
      x = 5
      Substituting ; y = 8
      ∴R is the pt (5,8)
    3.  
      coordinates answer 6c
    1. Gradient OA = Gradient of CB
      -1 – 0/2 – 0 = - ½
      Gradient of CB
      y – 3/0 – 4= - ½
      2y – 6 = 4
      2y = 10
      y = 5
    2.  
      coordinates answer 7b
    3.  
      coordinates answer 7c
      4AN = AC And A is a common point hence A, N, C lie on a straight line.
  6.  
    coordinates answer 8abc
    1. ∆ ABC line AB = 7 cm and BC = 8 cm ∡ ABC = 60o
      Construction of 60o
    2. AC = 7.6 + 0.1 and
      ACB = 53 + 1o
    3. 2 sides bisector 1
      Circle drawn radius 4.4. ± 0.1
    4. Bisect ACB
      Bisection line to cut the circle to identify P
      BPC BAC = 67o
      ∡ PBC = 88 ± 0.1o
    1.  
      coordinates answer 9a
      M (1+8/2, 1+10/2) = M (4.5, 5.5)
    2. AB: 4x – 5y = -1 x 2
      BC: 5x – 2y = 20 x 5
      8x – 10y = -2
      25x – 10y = 100
      -17x = -102
      x=102/17 = 6.0
      24 – 5y = -1
      5y = -25
      Y = 5
      B(6,5)
      x+ 6.0/2 = 4.5 x = 3
      y + 5/2 = 5.5 y = 6
      D (3,6)
    3. AB = √(16 – 1)2 + (5-1)2
      √25 + 16
      √41 = 6.40 (units)
  7. Mid ordinate
    Area = 1.2 (6.2 + 4.3 + 2.6)
    = 15.72

Download Coordinates and Graphs Questions and Answers - Form 1 Topical Mathematics.


Tap Here to Download for 50/-




Why download?

  • ✔ To read offline at any time.
  • ✔ To Print at your convenience
  • ✔ Share Easily with Friends / Students


Join our whatsapp group for latest updates
.
Subscribe now

access all the content at an affordable rate
or
Buy any individual paper or notes as a pdf via MPESA
and get it sent to you via WhatsApp

 

What does our community say about us?

Join our community on:

  • easyelimu app
  • Telegram
  • facebook page
  • twitter page
  • Pinterest