# Examples for secondary school students - page 60

1. Parabola 3 Find the equation of a parabola with its focus at (0,2) and its vertex at the origin. ?
2. Mother and daughter The mother is four times older than her daughter. Five years ago, her daughter was seven times younger than her mother. How many years do they have now?
3. Folded square ABCD is a square. The square is folded on the midpoint of AB and A is folded onto the fold, creating a shaded region. The perimiter of the shaded figure is 75. Find the area of square ABCD
4. Right triangle from axes A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment?
5. Hexagon cut pyramid Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge us 12 cm, and the side edge length is 41 cm.
6. Wagons and cranes Several of the same cranes unloaded 96 wagons. If there were 2 more cranes there would be less 8 wagons for each crane. How many cranes were here?
7. Free fall How long does the stone fall freely into a depth of 80m? What speed will it hit the bottom of the abyss?
8. Big number hat is the remainder when dividing number 10 to 47 - 111 by number 9?
9. ABCD AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD
10. Solve equation solve equation: ?
11. Combinations How many elements can form six times more combinations fourth class than combination of the second class?
12. Solid cuboid A solid cuboid has a volume of 40 cm3. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has length 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig.
13. Diagonals A diagonal of a rhombus is 20 cm long. If it's one side is 26 cm find the length of the other diagonal.
14. Cuboids Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633)
15. Trapezium internal angles A trapezium where AB is parallel to CD, has angle A : angle D = 4 :5, angle B = 3x-15 and angle C = 4x+20. Find angle A, B, C and D.
16. Box and whisker plot Construct a box and whisker plot for the given data. 56, 32, 54, 32, 23, 67, 23, 45, 12, 32, 34, 24, 36, 47, 19, 43
17. Circle - AG Find the coordinates of circle and its diameter if its equation is: ?
18. Equation of circle find an equation of the circle with indicated properties: a. center at (-3,5), diameter 20. b. center at origin and diameter 16.
19. How far From the top of a lighthouse 145 ft above sea level, the angle of depression of a boat 29°. How far is the boat from the lighthouse?
20. Equation of circle 2 Find the equation of a circle which touches the axis of y at a distance 4 from the origin and cuts off an intercept of length 6 on the axis x.

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