Daily Practice · Higher Plus
November 1983 5-a-day
Printing for a group?
The batch download puts all 5 tiers' November 1983 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1983
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 1983A bag holds 3 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd November 1983A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 0.6. How many values in total?
- 3rd November 1983Simplify sqrt(48) + sqrt(48), giving your answer in the form a sqrt(b).
- 4th November 1983Work out the coordinates of the turning point of y = x^2 + 10x + 2.
- 5th November 1983y is directly proportional to sqrt(x). When x = 16, y = 8. Work out y when x = 25.
- 6th November 1983The 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.
- 7th November 1983A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/36. Work out r.
- 8th November 1983On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 9th November 1983A rectangle is 22 cm by 26 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 10th November 1983Simplify (x^2 - 7x - 8)/(x - 8).
- 11th November 1983A train slows steadily from 29 m/s to rest in 10 seconds. Work out its deceleration.
- 12th November 1983In 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.
- 13th November 1983The probability of winning a game is 3/8. A player expects 6 wins. How many games did they play?
- 14th November 1983A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?
- 15th November 1983Expand and simplify (6 + sqrt(11))(6 - sqrt(11)).
- 16th November 1983In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 17th November 1983y is inversely proportional to x^2. When x = 4, y = 100. Work out y when x = 5.
- 18th November 1983In a vector proof you find that vector PQ = 6a - 3b and vector RS = 12a - 6b. What does this show about PQ and RS?
- 19th November 1983A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
- 20th November 1983On 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?
- 21st November 1983A block has mass 210 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.
- 22nd November 1983Make x the subject of 8x + 7 = y(x + 7).
- 23rd November 1983y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 24th November 1983A cuboid measures 7 cm by 6 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th November 1983A bag holds 6 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 26th November 1983A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 3. How many values in total?
- 27th November 1983x = 69 and y = 17, each correct to the nearest whole number. Work out the upper bound of x - y.
- 28th November 1983Write 7/(x - 5) + 5/(x + 6) as a single fraction.
- 29th November 1983y is directly proportional to sqrt(x). When x = 9, y = 9. Work out y when x = 81.
- 30th November 1983A cuboid measures 10 cm by 12 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.