Daily Practice · Higher Plus
January 1999 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 1999, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 1999 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1999
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1999Rationalise the denominator of 6/sqrt(3), giving your answer in its simplest form.
- 2nd January 1999Solve 6x^2 + 5x - 25 = 0.
- 3rd January 1999y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 4th January 1999A cuboid measures 3 cm by 4 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th January 1999A 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?
- 6th January 1999A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 1.4. How many values in total?
- 7th January 1999Simplify sqrt(50) + sqrt(8), giving your answer in the form a sqrt(b).
- 8th January 1999f(x) = 2x + 1. Work out the inverse function f^-1(x).
- 9th January 1999y is directly proportional to sqrt(x). When x = 4, y = 14. Work out y when x = 16.
- 10th January 1999A cuboid measures 9 cm by 4 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th January 1999A bag holds 4 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 12th January 1999On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 13th January 1999A rectangle is 30 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 14th January 1999Solve x^2 + y^2 = 225 and y = x - 3 simultaneously.
- 15th January 1999A train slows steadily from 28 m/s to rest in 4 seconds. Work out its deceleration.
- 16th January 1999The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 17th January 1999A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 18th January 1999A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 3. How many values in total?
- 19th January 1999Expand and simplify (8 + sqrt(7))(8 - sqrt(7)).
- 20th January 1999Use the iteration x(n+1) = cube root of (6x(n) + 7) with x(0) = 3. Work out x(1) to 3 decimal places.
- 21st January 1999y is inversely proportional to x^2. When x = 2, y = 16. Work out y when x = 4.
- 22nd January 1999In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 23rd January 1999The probability of winning a game is 1/10. A player expects 14 wins. How many games did they play?
- 24th January 1999On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 25th January 1999A block has mass 760 g (to the nearest 10 g) and volume 6 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 26th January 1999Work out the nth term of the quadratic sequence 10, 18, 28, 40, ...
- 27th January 1999y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 3.
- 28th January 1999In a vector proof you find that vector PQ = a - 5b and vector RS = 3a - 15b. What does this show about PQ and RS?
- 29th January 1999A bag holds 4 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 30th January 1999A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
- 31st January 1999x = 87 and y = 22, each correct to the nearest whole number. Work out the upper bound of x - y.