Daily Practice · Higher Plus
January 1990 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1990 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1990
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1990Simplify (x^2 - 11x + 30)/(x - 6).
- 2nd January 1990y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 3rd January 1990The 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.
- 4th January 1990A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 6/55. Work out r.
- 5th January 1990A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 0.6. How many values in total?
- 6th January 1990A car covers 720 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.
- 7th January 1990In an algebraic proof, how would you write the square of an odd number in terms of an integer n?
- 8th January 1990y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 9.
- 9th January 1990In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 10th January 1990The probability of winning a game is 3/8. A player expects 45 wins. How many games did they play?
- 11th January 1990On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 12th January 1990Rationalise the denominator of 48/sqrt(6), giving your answer in its simplest form.
- 13th January 1990Make x the subject of 6x + 2 = y(x + 2).
- 14th January 1990A train slows steadily from 16 m/s to rest in 4 seconds. Work out its deceleration.
- 15th January 1990In a vector proof you find that vector PQ = 3a + 6b and vector RS = 6a + 12b. What does this show about PQ and RS?
- 16th January 1990A bag holds 4 red and n blue counters. The probability of taking a red is 4/11. Work out n.
- 17th January 1990A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?
- 18th January 1990Simplify sqrt(32) + sqrt(32), giving your answer in the form a sqrt(b).
- 19th January 1990Write 2/(x - 6) + 5/(x - 2) as a single fraction.
- 20th January 1990y is inversely proportional to x^2. When x = 3, y = 25. Work out y when x = 5.
- 21st January 1990A cuboid measures 6 cm by 3 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd January 1990A bag holds 3 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 23rd January 1990On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 24th January 1990A rectangle is 30 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 25th January 1990Solve 15x^2 - 14x - 8 = 0.
- 26th January 1990y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.
- 27th January 1990A cuboid measures 10 cm by 12 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th January 1990A bag holds 6 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 29th January 1990A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 3.5. How many values in total?
- 30th January 1990Expand and simplify (8 + sqrt(5))(8 - sqrt(5)).
- 31st January 1990f(x) = 6x - 2. Work out the inverse function f^-1(x).