# Examples for secondary school students

1. Average age The average age of all people at the celebration was equal to the number of people present. After the departure of one person who was 29 years old, average age was again equal to the number present. How many people were originally to celebrate?
2. 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. What is the slope of a ladder 6.2 m long and 5.12 m in height.
4. Right angled triangle 2 LMN is a right angled triangle with vertices at L(1,3), M(3,5) and N(6,n). Given angle LMN is 90° find n
5. US GDP Consider the following dataset , which contsins the domestic US gross in millions of the top grossing movie over the last 5 years. 300,452,513,550,780 I. Find the Mean of the Dataset II. Find the Squared deviation of the second observation from the mean
6. Exponential equation Solve for x: (4^x):0,5=2/64.
7. Geometric seq Find the third member of geometric progression if a1 + a2 = 36 and a1 + a3 = 90. Calculate its quotient.
8. The mast A 40 m high mast is secured in half by eight ropes of 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance.
9. ABCD AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD
10. The pool The pool has a volume of 40 m3 and the water temperature is 20 °C. How much water at 100 °C should we pour into the pool to increase the water temperature by 5 °C?
11. Warehouses In the three warehouses, a total of 70 tons of grain was stored. In the second warehouse was stored 8.5t less and in the third 3.5t more than in the first. How many tons of grain was stored in each warehouse?
12. Debt Joe and Caryl have a debt of \$100,500. Joe makes \$90,000 per year, and Caryl makes \$35,000 per year. How much should both pay to zero out the debt fairly, based on their salaries?
13. Perimeter of triangle In triangle ABC angle A is 60° angle B is 90° side size c is 15 cm. Calculate the triangle circumference.
14. Sum or product What is the probability that two dice fall will have the sum 7 or product 12?
15. Sum on dice We have two dice. What is the greater likelihood of fall a total sum 7 or 8 ? (write 7, 8 or 0 if the probabilities are the same)?
16. Triangle KLM In the rectangular triangle KLM, where is hypotenuse m (sketch it!) find the length of the leg k and the height of triangle h if hypotenuse's segments are known mk = 5cm and ml = 15cm
17. Isosceles triangle The perimeter of an isosceles triangle is 112 cm. The length of the arm to the length of the base is at ratio 5:6. Find the triangle area.
18. Diagonal 20 Diagonal pathway for the rectangular town plaza whose length is 20 m longer than the width. if the pathway is 20 m shorter than twice the width. How long should the pathway be?
19. Lines How many lines can be draw with 8 points, if three points lie on one line and the other any three points do not lie on the same line?
20. Digits How many five-digit numbers can be written from numbers 0.3,4, 5, 7 that is divided by 10 and if digits can be repeated.

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