Daily Practice · Higher Plus
January 1998 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 1998, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 1998 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1998
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1998f(x) = 5x - 4 and g(x) = 4x + 1. Work out fg(5).
- 2nd January 1998y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
- 3rd January 1998In a vector proof you find that vector PQ = a + 5b and vector RS = 2a + 10b. What does this show about PQ and RS?
- 4th January 1998A bag holds 5 red and n blue counters. The probability of taking a red is 5/9. Work out n.
- 5th January 1998On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 6th January 1998Expand and simplify (6 + sqrt(3))(6 - sqrt(3)).
- 7th January 1998The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 8th January 1998y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 9th January 1998A cuboid measures 7 cm by 5 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th January 1998A bag holds 7 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th January 1998A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 3. How many values in total?
- 12th January 1998A block has mass 220 g (to the nearest 10 g) and volume 21 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 13th January 1998A quadratic sequence starts 2, 11, 24, 41. Work out the second difference, and the coefficient of n^2.
- 14th January 1998y is directly proportional to sqrt(x). When x = 36, y = 30. Work out y when x = 81.
- 15th January 1998A cuboid measures 5 cm by 14 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th January 1998A bag holds 4 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th January 1998On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 18th January 1998x = 186 and y = 8, each correct to the nearest whole number. Work out the upper bound of x - y.
- 19th January 1998Solve x^2 + 4x + 3 < 0.
- 20th January 1998A train slows steadily from 35 m/s to rest in 8 seconds. Work out its deceleration.
- 21st January 1998The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 22nd January 1998A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 7/22. Work out r.
- 23rd January 1998A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 3.5. How many values in total?
- 24th January 1998A car covers 170 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 25th January 1998Write x^2 + 10x + 4 in the form (x + a)^2 + b.
- 26th January 1998y is inversely proportional to x^2. When x = 5, y = 4. Work out y when x = 2.
- 27th January 1998In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 28th January 1998The probability of winning a game is 4/5. A player expects 40 wins. How many games did they play?
- 29th January 1998On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 30th January 1998Rationalise the denominator of 18/sqrt(3), giving your answer in its simplest form.
- 31st January 1998Work out the coordinates of the turning point of y = x^2 - 2x - 5.