Daily Practice · Higher Plus
November 1990 5-a-day
Printing for a group?
The batch download puts all 5 tiers' November 1990 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1990
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 1990A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 0.6. How many values in total?
- 2nd November 1990Rationalise the denominator of 15/sqrt(5), giving your answer in its simplest form.
- 3rd November 1990Simplify (x^2 - 4)/(x + 2).
- 4th November 1990y is inversely proportional to x^2. When x = 3, y = 144. Work out y when x = 6.
- 5th November 1990In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 6th November 1990The probability of winning a game is 1/5. A player expects 4 wins. How many games did they play?
- 7th November 1990On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 8th November 1990Simplify sqrt(8) + sqrt(2), giving your answer in the form a sqrt(b).
- 9th November 1990In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 10th November 1990y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 2.
- 11th November 1990In a vector proof you find that vector PQ = 3a + 3b and vector RS = 9a + 9b. What does this show about PQ and RS?
- 12th November 1990A bag holds 6 red and n blue counters. The probability of taking a red is 3/4. Work out n.
- 13th November 1990A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 0.6. How many values in total?
- 14th November 1990A rectangle is 12 cm by 14 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 15th November 1990Make x the subject of 8x + 2 = y(x + 2).
- 16th November 1990y is directly proportional to sqrt(x). When x = 16, y = 16. Work out y when x = 4.
- 17th November 1990A cuboid measures 4 cm by 11 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 18th November 1990A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 19th November 1990On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 20th November 1990Expand and simplify (7 + sqrt(5))(7 - sqrt(5)).
- 21st November 1990Write 2/(x - 5) + 6/(x + 5) as a single fraction.
- 22nd November 1990A train slows steadily from 35 m/s to rest in 5 seconds. Work out its deceleration.
- 23rd November 1990A cuboid measures 5 cm by 11 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 24th November 1990A bag holds 4 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 25th November 1990A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 26th November 1990A block has mass 710 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 27th November 1990Solve 16x^2 - 9 = 0.
- 28th November 1990y is inversely proportional to x^2. When x = 2, y = 32. Work out y when x = 4.
- 29th November 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.
- 30th November 1990A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.