Daily Practice · Higher Plus
November 2006 - Higher Plus 5-a-day
Every Higher Plus sheet published in November 2006, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' November 2006 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 2006
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 2006A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 0.6. How many values in total?
- 2nd November 2006Simplify sqrt(80) + sqrt(180), giving your answer in the form a sqrt(b).
- 3rd November 2006f(x) = 7x - 8. Work out the inverse function f^-1(x).
- 4th November 2006y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 64.
- 5th November 2006The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 6th November 2006A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 7th November 2006On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 8th November 2006A rectangle is 18 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 9th November 2006Solve x^2 + y^2 = 225 and y = x - 3 simultaneously.
- 10th November 2006A train slows steadily from 23 m/s to rest in 10 seconds. Work out its deceleration.
- 11th November 2006In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 12th November 2006The probability of winning a game is 3/4. A player expects 6 wins. How many games did they play?
- 13th November 2006A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 1.4. How many values in total?
- 14th November 2006Expand and simplify (7 + sqrt(7))(7 - sqrt(7)).
- 15th November 2006Use the iteration x(n+1) = cube root of (4x(n) + 3) with x(0) = 3. Work out x(1) to 3 decimal places.
- 16th November 2006y is inversely proportional to x^2. When x = 3, y = 100. Work out y when x = 5.
- 17th November 2006In a vector proof you find that vector PQ = 2a + 6b and vector RS = 8a + 24b. What does this show about PQ and RS?
- 18th November 2006A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
- 19th November 2006On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 20th November 2006A block has mass 250 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 21st November 2006Work out the nth term of the quadratic sequence 4, 13, 30, 55, ...
- 22nd November 2006y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
- 23rd November 2006A cuboid measures 10 cm by 11 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th November 2006A bag holds 4 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 25th November 2006A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 1.4. How many values in total?
- 26th November 2006x = 177 and y = 58, each correct to the nearest whole number. Work out the upper bound of x - y.
- 27th November 2006The point (2, -6) lies on y = f(x). Write down its image on y = -f(x).
- 28th November 2006y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 36.
- 29th November 2006A cuboid measures 4 cm by 7 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 30th November 2006A bag holds 6 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?