Daily Practice · Higher Plus
January 2002 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2002, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2002 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2002
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2002A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/11. Work out r.
- 2nd January 2002A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 0.6. How many values in total?
- 3rd January 2002Simplify sqrt(32) + sqrt(18), giving your answer in the form a sqrt(b).
- 4th January 2002Simplify (x^2 + 11x + 28)/(x + 7).
- 5th January 2002y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 3.
- 6th January 2002In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 7th January 2002The probability of winning a game is 1/5. A player expects 7 wins. How many games did they play?
- 8th January 2002On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 9th January 2002A rectangle is 13 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 10th January 2002In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 11th January 2002y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 12th January 2002In a vector proof you find that vector PQ = 6a + 5b and vector RS = 12a + 10b. What does this show about PQ and RS?
- 13th January 2002A bag holds 5 red and n blue counters. The probability of taking a red is 5/8. Work out n.
- 14th January 2002A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 0.6. How many values in total?
- 15th January 2002Expand and simplify (2 + sqrt(6))(2 - sqrt(6)).
- 16th January 2002Make x the subject of 4x + 7 = y(x + 7).
- 17th January 2002y is directly proportional to sqrt(x). When x = 4, y = 18. Work out y when x = 16.
- 18th January 2002A cuboid measures 3 cm by 13 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 19th January 2002A bag holds 9 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 20th January 2002On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 21st January 2002A block has mass 300 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 22nd January 2002Write 4/(x + 3) + 2/(x - 5) as a single fraction.
- 23rd January 2002A train slows steadily from 37 m/s to rest in 10 seconds. Work out its deceleration.
- 24th January 2002A cuboid measures 4 cm by 4 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 25th January 2002A bag holds 4 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 26th January 2002A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 27th January 2002x = 189 and y = 169, each correct to the nearest whole number. Work out the upper bound of x - y.
- 28th January 2002Solve 4x^2 + 23x - 6 = 0.
- 29th January 2002y is inversely proportional to x^2. When x = 4, y = 9. Work out y when x = 3.
- 30th January 2002The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 31st January 2002A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 7/22. Work out r.